@article {SIA-2021,
    AUTHOR = {Agafonov, Sergey I.},
     TITLE = {Quadratic integrals of geodesic flow, webs, and integrable
              billiards},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {161},
      YEAR = {2021},
     PAGES = {104041, 7~pages},
       DOI = {10.1016/j.geomphys.2020.104041},
       URL = {https://doi.org/10.1016/j.geomphys.2020.104041},
    EPRINT = {2004.12374},
}

@incollection {A-L-V,
    AUTHOR = {Alekseevskij, D. V. and Vinogradov, A. M. and Lychagin, V. V.},
     TITLE = {Basic ideas and concepts of differential geometry},
 BOOKTITLE = {Geometry,~{I}},
    EDITOR = {Gamkrelidze, R. V.},
    SERIES = {Encyclopaedia Math. Sci.},
    VOLUME = {28},
     PAGES = {1--264},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1991},
}

@book {AA,
    AUTHOR = {Aoust, A.},
     TITLE = {Analyse infinit\'esimale des courbes trac\'ees sur une surface
              quelconque},
 PUBLISHER = {Gauthier-Villars, Paris},
      YEAR = {1869},
     PAGES = {vi+314},
}

@article {B-M-2009,
    AUTHOR = {Baran, Hynek and Marvan, Michal},
     TITLE = {On integrability of {W}eingarten surfaces: a~forgotten class},
   JOURNAL = {J.~Phys.~A},
  FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
    VOLUME = {42},
      YEAR = {2009},
    NUMBER = {40},
     PAGES = {404007, 16~pages},
       DOI = {10.1088/1751-8113/42/40/404007},
       URL = {https://doi.org/10.1088/1751-8113/42/40/404007},
    EPRINT = {1002.0989},
}

@article {B-M-2010,
    AUTHOR = {Baran, Hynek and Marvan, Michal},
     TITLE = {Classification of integrable {W}eingarten surfaces possessing
              an {$\mathfrak{sl}(2)$}-valued zero curvature representation},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {23},
      YEAR = {2010},
    NUMBER = {10},
     PAGES = {2577--2597},
       DOI = {10.1088/0951-7715/23/10/013},
       URL = {https://doi.org/10.1088/0951-7715/23/10/013},
    EPRINT = {1002.0992},
}

@article {B-F-F-H,
    AUTHOR = {Barnhill, R. E. and Farin, G. and Fayard, L. and Hagen, H.},
     TITLE = {Twists, curvatures and surface interrogation},
   JOURNAL = {Comput. Aided Des.},
  FJOURNAL = {Computer-Aided Design},
    VOLUME = {20},
      YEAR = {1988},
    NUMBER = {6},
     PAGES = {341--344, 345--346},
       DOI = {10.1016/0010-4485(88)90116-9},
       URL = {https://doi.org/10.1016/0010-4485(88)90116-9},
}

@article {Beetle,
    AUTHOR = {Beetle, R. D.},
     TITLE = {A~formula in the theory of surfaces},
   JOURNAL = {Ann. of Math.},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {15},
      YEAR = {1913--1914},
    NUMBER = {1--4},
     PAGES = {179--183},
       DOI = {10.2307/1967816},
       URL = {https://doi.org/10.2307/1967816},
}

@book {LB-I,
    AUTHOR = {Bianchi, Luigi},
     TITLE = {Lezioni di Geometria Differenziale, Vol.~1},
 PUBLISHER = {E.~Spoerri, Pisa},
      YEAR = {1902},
}

@book {LB-II,
    AUTHOR = {Bianchi, Luigi},
     TITLE = {Lezioni di Geometria Differenziale, Vol.~2},
 PUBLISHER = {E.~Spoerri, Pisa},
      YEAR = {1903},
}

@article {LB-1922,
    AUTHOR = {Bianchi, Luigi},
     TITLE = {Le reti di {T}chebychef sulle superficie ed il parallelismo nel
              senso di {L}evi-{C}ivita},
   JOURNAL = {Boll. Unione Mat. Ital.},
  FJOURNAL = {Bollettino dell'Unione Matematica Italiana},
    VOLUME = {1},
      YEAR = {1922},
     PAGES = {1--6},
}

@incollection {Bob,
    AUTHOR = {Bobenko, Alexander I.},
     TITLE = {Surfaces in terms of~{$2$} by~{$2$} matrices. {O}ld and new
              integrable cases},
 BOOKTITLE = {Harmonic Maps and Integrable Systems},
    EDITOR = {Fordy, A. P. and Wood, J. C.},
    SERIES = {Aspects Math.},
    VOLUME = {E23},
     PAGES = {83--127},
 PUBLISHER = {Friedr. Vieweg, Braunschweig},
      YEAR = {1994},
       DOI = {10.1007/978-3-663-14092-4\_5},
       URL = {https://doi.org/10.1007/978-3-663-14092-4_5},
}

@incollection {AB-UP,
    AUTHOR = {Bobenko, Alexander I. and Pinkall, Ulrich},
     TITLE = {Discretization of surfaces and integrable systems},
 BOOKTITLE = {Discrete Integrable Geometry and Physics ({V}ienna, 1996)},
    EDITOR = {Bobenko, A. I. and Seiler, R.},
    SERIES = {Oxford Lecture Ser. Math. Appl.},
    VOLUME = {16},
     PAGES = {3--58},
 PUBLISHER = {Oxford University Press, New York},
      YEAR = {1999},
}

@article {B-P-R,
    AUTHOR = {Bobenko, Alexander I. and Pottmann, Helmut and R\"orig, Thilo},
     TITLE = {Multi-nets. {C}lassification of discrete and smooth surfaces
              with characteristic properties on arbitrary parameter
              rectangles},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {63},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {624--655},
       DOI = {10.1007/s00454-019-00101-1},
       URL = {https://doi.org/10.1007/s00454-019-00101-1},
    EPRINT = {1802.05063},
}

@book {B-S,
    AUTHOR = {Bobenko, Alexander I. and Suris, Yuri B.},
     TITLE = {Discrete differential geometry. Integrable structure},
    SERIES = {Grad. Stud. Math.},
    VOLUME = {98},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {xxiv+404},
       DOI = {10.1090/gsm/098},
       URL = {https://doi.org/10.1090/gsm/098},
}

@article {EB-1925,
    AUTHOR = {Bortolotti, Enea},
     TITLE = {Su alcune questioni di geometria delle superficie},
   JOURNAL = {Boll. Unione Mat. Ital},
  FJOURNAL = {Bollettino dell'Unione Matematica Italiana},
    VOLUME = {4},
      YEAR = {1925},
     PAGES = {162--166},
}

@article {DB-2017,
    AUTHOR = {Brander, David},
     TITLE = {Pseudospherical surfaces with singularities},
   JOURNAL = {Ann. Mat. Pura Appl.},
  FJOURNAL = {Annali di Matematica Pura ed Applicata. Series IV},
    VOLUME = {196},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {905--928},
       DOI = {10.1007/s10231-016-0601-8},
       URL = {https://doi.org/10.1007/s10231-016-0601-8},
    EPRINT = {1502.04876},
}

@article {B-T-1995,
    AUTHOR = {Bruce, J. W. and Tari, F.},
     TITLE = {On binary differential equations},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {8},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {255--271},
       DOI = {10.1088/0951-7715/8/2/008},
       URL = {https://doi.org/10.1088/0951-7715/8/2/008},
}

@article {PLC,
    AUTHOR = {Chebyshev, P. L.},
     TITLE = {On the cutting of garments},
   JOURNAL = {Russian Math. Surveys},
  FJOURNAL = {Russian Mathematical Surveys},
    VOLUME = {1},
      YEAR = {1946},
    NUMBER = {2(12)},
     PAGES = {no.~2, 38--42},
}

@article {C-T-1981,
    AUTHOR = {Chern, Shiing-Shen and Tenenblat, Keti},
     TITLE = {Foliations on a~surface of constant curvature and the modified
              {K}orteweg--de {V}ries equations},
   JOURNAL = {J.~Differential Geometry},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {16},
      YEAR = {1981},
    NUMBER = {3},
     PAGES = {347--349},
       DOI = {10.4310/jdg/1214436216},
       URL = {https://doi.org/10.4310/jdg/1214436216},
}

@article {JC-1993,
    AUTHOR = {Cie\'sli\'nski, Jan},
     TITLE = {Nonlocal symmetries and a~working algorithm to isolate
              integrable geometries},
   JOURNAL = {J.~Phys.~A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {26},
      YEAR = {1993},
    NUMBER = {5},
     PAGES = {L267--L271},
       DOI = {10.1088/0305-4470/26/5/017},
       URL = {https://doi.org/10.1088/0305-4470/26/5/017},
}

@article {C-G-S,
    AUTHOR = {Cie\'sli\'nski, Jan and Goldstein, Piotr and Sym, Antoni},
     TITLE = {Isothermic surfaces in {$\mathbf{E}^3$} as soliton surfaces},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {205},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {37--43},
       DOI = {10.1016/0375-9601(95)00504-V},
       URL = {https://doi.org/10.1016/0375-9601(95)00504-V},
    EPRINT = {solv-int/9502004},
}

@book {GD-I,
    AUTHOR = {Darboux, Gaston},
     TITLE = {Le\c{c}ons sur la th\'eorie g\'en\'erale des surfaces, Premi\`ere Partie},
 PUBLISHER = {Gauthier-Villars, Paris},
      YEAR = {1887},
}

@book {GD-II,
    AUTHOR = {Darboux, Gaston},
     TITLE = {Le\c{c}ons sur la th\'eorie g\'en\'erale des surfaces, Deuxi\`eme Partie},
 PUBLISHER = {Gauthier-Villars, Paris},
      YEAR = {1889},
}

@book {GD-III,
    AUTHOR = {Darboux, Gaston},
    AUTHOR = {Darboux, Gaston},
     TITLE = {Le\c{c}ons sur la th\'eorie g\'en\'erale des surfaces, Troisi\`eme Partie},
 PUBLISHER = {Gauthier-Villars, Paris},
      YEAR = {1894},
}

@article {AMD,
    AUTHOR = {D\'ecaillot, Anne-Marie},
     TITLE = {G\'eom\'etrie des tissus. {M}osa\"{\i}ques. \'Echiquiers. {M}ath\'ematiques
              curieuses et utiles},
   JOURNAL = {Rev. Histoire Math.},
  FJOURNAL = {Revue d'Histoire des Math\'ematiques. Journal for the History of
              Mathematics},
    VOLUME = {8},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {145--206},
}

@article {UD-1870,
    AUTHOR = {Dini, Ulisse},
     TITLE = {Sopra alcune formole generali della teoria delle superficie,
              e loro applicazioni},
   JOURNAL = {Ann. Mat. Pura Appl.},
  FJOURNAL = {Annali di Matematica Pura ed Applicata},
    VOLUME = {4},
      YEAR = {1870},
     PAGES = {175--206},
       DOI = {10.1007/BF02420031},
       URL = {https://doi.org/10.1007/BF02420031},
}

@article {YaSD,
    AUTHOR = {Dubnov, Ya. S.},
     TITLE = {Semitensors of a~two-dimensional net},
   JOURNAL = {Izv. Vyssh. Uchebn. Zaved. Mat.},
  FJOURNAL = {Izvestija Vys\v{s}ih U\v{c}ebnyh Zavedeni\u{\i} Matematika},
      YEAR = {1958},
    NUMBER = {3(4)},
     PAGES = {no.~3, 74--83},
}

@article {BAD-1981,
    AUTHOR = {Dubrovin, B. A.},
     TITLE = {Theta-functions and nonlinear equations},
   JOURNAL = {Russian Math. Surveys},
  FJOURNAL = {Russian Mathematical Surveys},
    VOLUME = {36},
      YEAR = {1981},
    NUMBER = {2},
     PAGES = {no.~2, 11--92},
       DOI = {10.1070/RM1981v036n02ABEH002596},
       URL = {https://doi.org/10.1070/RM1981v036n02ABEH002596},
}

@article {LPE-1904,
    AUTHOR = {Eisenhart, Luther Pfahler},
     TITLE = {Three particular systems of lines on a~surface},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {5},
      YEAR = {1904},
    NUMBER = {4},
     PAGES = {421--437},
       DOI = {10.2307/1986272},
       URL = {https://doi.org/10.2307/1986272},
}

@book {LPE-1909,
    AUTHOR = {Eisenhart, Luther Pfahler},
     TITLE = {A~treatise on the differential geometry of curves and
              surfaces},
 PUBLISHER = {Ginn, Boston},
      YEAR = {1909},
     PAGES = {xiv+474},
}

@book {F-P-1979,
    AUTHOR = {Faux, Ivor D. and Pratt, Michael J.},
     TITLE = {Computational geometry for design and manufacture},
    SERIES = {Math. Appl.},
 PUBLISHER = {Ellis Horwood, Chichester},
      YEAR = {1979},
     PAGES = {329},
}

@article {DCF-LAOS,
    AUTHOR = {Catalano Ferraioli, D. and de Oliveira Silva, L. A.},
     TITLE = {Nontrivial 1-parameter families of zero-curvature
              representations obtained via symmetry actions},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {94},
      YEAR = {2015},
     PAGES = {185--198},
       DOI = {10.1016/j.geomphys.2015.04.001},
       URL = {https://doi.org/10.1016/j.geomphys.2015.04.001},
}

@book {F-T-2007,
    AUTHOR = {Fuchs, Dmitry and Tabachnikov, Serge},
     TITLE = {Mathematical omnibus. Thirty lectures on classic mathematics},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2007},
     PAGES = {xvi+463},
       DOI = {10.1090/mbk/046},
       URL = {https://doi.org/10.1090/mbk/046},
}

@article {BG,
    AUTHOR = {Gambier, Bertrand},
     TITLE = {Surfaces de {V}oss-{G}uichard},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup.},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Troisi\`eme
              S\'erie},
    VOLUME = {48},
      YEAR = {1931},
     PAGES = {359--396},
       DOI = {10.24033/asens.813},
       URL = {https://doi.org/10.24033/asens.813},
}

@article {Ghy,
    AUTHOR = {Ghys, \'Etienne},
     TITLE = {Sur la coupe des v\^etements: variation autour d'un th\`eme de
              {T}chebychev},
   JOURNAL = {Enseign. Math.},
  FJOURNAL = {L'Enseignement Math\'ematique. Revue Internationale. 2e S\'erie},
    VOLUME = {57},
      YEAR = {2011},
    NUMBER = {1-2},
     PAGES = {165--208},
       DOI = {10.4171/LEM/57-1-8},
       URL = {https://doi.org/10.4171/LEM/57-1-8},
}

@article {WCG-1922,
    AUTHOR = {Graustein, W. C.},
     TITLE = {Parallel maps of surfaces},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {23},
      YEAR = {1922},
    NUMBER = {3},
     PAGES = {298--332},
       DOI = {10.2307/1988813},
       URL = {https://doi.org/10.2307/1988813},
}

@article {WCG-1932,
    AUTHOR = {Graustein, W. C.},
     TITLE = {Parallelism and equidistance in classical differential
              geometry},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {34},
      YEAR = {1932},
    NUMBER = {3},
     PAGES = {557--593},
       DOI = {10.2307/1989367},
       URL = {https://doi.org/10.2307/1989367},
}

@article {GMG,
    AUTHOR = {Green, G. M.},
     TITLE = {Nets of space curves},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {21},
      YEAR = {1920},
    NUMBER = {2},
     PAGES = {207--236},
       DOI = {10.2307/1988903},
       URL = {https://doi.org/10.2307/1988903},
}

@incollection {G-T,
    AUTHOR = {G\"urses, Metin and Tek, S\"uleyman},
     TITLE = {Integrable curves and surfaces},
 BOOKTITLE = {Proceedings of the 17th International Conference ``Geometry, Integrability and Quantization'' (Sts. Constantine and Elena, June 5--10, 2015)},
    EDITOR = {Mladenov, I. M. and Meng, Guowu and Yoshioka, A.},
    SERIES = {Geom. Integrability Quantization},
    VOLUME = {17},
     PAGES = {13--71},
 PUBLISHER = {Bulgarian Academy of Sciences, Sofia},
      YEAR = {2016},
       DOI = {10.7546/giq-17-2016-13-71},
       URL = {https://doi.org/10.7546/giq-17-2016-13-71},
}

@article {HH-1972,
    AUTHOR = {Hasimoto, Hidenori},
     TITLE = {A~soliton on a~vortex filament},
   JOURNAL = {J.~Fluid Mech.},
  FJOURNAL = {Journal of Fluid Mechanics},
    VOLUME = {51},
      YEAR = {1972},
    NUMBER = {3},
     PAGES = {477--485},
       DOI = {10.1017/S0022112072002307},
       URL = {https://doi.org/10.1017/S0022112072002307},
}

@article {H-O-O,
    AUTHOR = {Howell, P. D. and Ockendon, H. and Ockendon, J. R.},
     TITLE = {Draping woven sheets},
   JOURNAL = {ANZIAM~J.},
  FJOURNAL = {The ANZIAM Journal. The Australian \& New Zealand Industrial
              and Applied Mathematics Journal},
    VOLUME = {62},
      YEAR = {2020},
    NUMBER = {4},
     PAGES = {355--385},
       DOI = {10.1017/S144618112000019X},
       URL = {https://doi.org/10.1017/S144618112000019X},
}

@book {VFK-II,
    AUTHOR = {Kagan, V. F.},
     TITLE = {Fundamentals of the theory of surfaces in tensorial
              representation~{II}},
 PUBLISHER = {Gostechizdat, Moskva},
      YEAR = {1948},
}

@article {K-T-2021,
    AUTHOR = {Khesin, Boris and Tabachnikov, Serge},
     TITLE = {Polar bear or penguin? {M}usings on earth cartography and
              {C}hebyshev nets},
   JOURNAL = {Math. Intelligencer},
  FJOURNAL = {The Mathematical Intelligencer},
    VOLUME = {43},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {20--24},
       DOI = {10.1007/s00283-020-10013-1},
       URL = {https://doi.org/10.1007/s00283-020-10013-1},
}

@article {K-M-T,
    AUTHOR = {Kilian, Martin and M\"uller, Christian and Tervooren, Jonas},
     TITLE = {Smooth and discrete cone-nets},
   JOURNAL = {Results Math.},
  FJOURNAL = {Results in Mathematics},
    VOLUME = {78},
      YEAR = {2023},
    NUMBER = {3},
     PAGES = {110, 40~pages},
       DOI = {10.1007/s00025-023-01884-9},
       URL = {https://doi.org/10.1007/s00025-023-01884-9},
}

@article {RK-1979,
    AUTHOR = {Koch, Richard},
     TITLE = {Parallelogrammnetze},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {86},
      YEAR = {1979},
    NUMBER = {4},
     PAGES = {265--284},
       DOI = {10.1007/BF01300243},
       URL = {https://doi.org/10.1007/BF01300243},
}

@article {RK-1982,
    AUTHOR = {Koch, Richard},
     TITLE = {Diagonale {T}schebyscheff--{N}etze},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"at
              Hamburg},
    VOLUME = {52},
      YEAR = {1982},
     PAGES = {43--66},
       DOI = {10.1007/BF02941865},
       URL = {https://doi.org/10.1007/BF02941865},
}

@article {BGK-1993,
    AUTHOR = {Konopel'chenko, B. G.},
     TITLE = {Nets in {$\mathbb{R}^3$}, their integrable evolutions and the
              {DS} hierarchy},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {183},
      YEAR = {1993},
    NUMBER = {2-3},
     PAGES = {153--159},
       DOI = {10.1016/0375-9601(93)91162-X},
       URL = {https://doi.org/10.1016/0375-9601(93)91162-X},
}

@article {K-M,
    AUTHOR = {Krasil'shchik, Joseph and Marvan, Michal},
     TITLE = {Coverings and integrability of the
              {G}auss--{M}ainardi--{C}odazzi equations},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {56},
      YEAR = {1999},
    NUMBER = {2--3},
     PAGES = {217--230},
       DOI = {10.1023/A:1006121716159},
       URL = {https://doi.org/10.1023/A:1006121716159},
    EPRINT = {solv-int/9812010},
}

@book {ENK,
    AUTHOR = {Kuznetsov, E. N.},
     TITLE = {Underconstrained structural systems},
    SERIES = {Mech. Engrg. Ser.},
 PUBLISHER = {Springer, New York},
      YEAR = {1991},
     PAGES = {xiii+312},
       DOI = {10.1007/978-1-4612-3176-9},
       URL = {https://doi.org/10.1007/978-1-4612-3176-9},
}

@article {GLL-1977,
    AUTHOR = {Lamb, Jr., G. L.},
     TITLE = {Solitons on moving space curves},
   JOURNAL = {J.~Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {18},
      YEAR = {1977},
    NUMBER = {8},
     PAGES = {1654--1661},
       DOI = {10.1063/1.523453},
       URL = {https://doi.org/10.1063/1.523453},
}

@mics {L-S-T,
    AUTHOR = {Levi, D. and Sym, A. and Tu, G.-Z.},
     TITLE = {A~working algorithm to isolate integrable surfaces in $E^3$},
      NOTE = {{P}reprint DF INFN Roma 761, 1990},
}

@article {IL-2015,
    AUTHOR = {Liddell, I.},
     TITLE = {Frei {O}tto and the development of gridshells},
   JOURNAL = {Case Stud. Struct. Eng.},
  FJOURNAL = {Case Studies in Structural Engineering},
    VOLUME = {4},
      YEAR = {2015},
     PAGES = {39--49},
       DOI = {10.1016/j.csse.2015.08.001},
       URL = {https://doi.org/10.1016/j.csse.2015.08.001},
}

@article {SL-1878,
    AUTHOR = {Lie, Sophus},
     TITLE = {Beitr\"age zur {T}heorie der {M}inimalfl\"achen.~{I}. {P}rojectivische {U}ntersuchungen \"uber algebraische {M}inimalfl\"achen},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {14},
      YEAR = {1878},
    NUMBER = {3},
     PAGES = {331--416},
       DOI = {10.1007/BF01677141},
       URL = {https://doi.org/10.1007/BF01677141},
}

@incollection {RvL,
    AUTHOR = {von Lilienthal, R.},
     TITLE = {Die auf einer Fl\"ache gezogenen Kurven},
 BOOKTITLE = {Enzyklop\"adie der Mathematischen Wissenschaften mit Einschlu{\ss} ihrer Anwendungen},
     PAGES = {105--183.},
 PUBLISHER = {Teubner, Leipzig},
      YEAR = {1902},
}

@article {RL-RC,
    AUTHOR = {Lin, Runliang and Conte, Robert},
     TITLE = {On a~surface isolated by {G}ambier},
   JOURNAL = {J.~Nonlinear Math. Phys.},
  FJOURNAL = {Journal of Nonlinear Mathematical Physics},
    VOLUME = {25},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {509--514},
       DOI = {10.1080/14029251.2018.1503393},
       URL = {https://doi.org/10.1080/14029251.2018.1503393},
    EPRINT = {1805.10450},
}

@article {DL-2023,
    AUTHOR = {Liu, D. and Pellis, D. and Chiang, Y.-C. and Rist, F. and
              Wallner, J. and Pottmann, H.},
     TITLE = {Deployable strip structures},
   JOURNAL = {ACM Trans. Graph.},
  FJOURNAL = {ACM Transactions on Graphics},
    VOLUME = {42},
      YEAR = {2023},
    NUMBER = {4},
     PAGES = {103, 16~pages},
       DOI = {10.1145/3592393},
       URL = {https://doi.org/10.1145/3592393},
}

@article {M-T-1956,
    AUTHOR = {Mack, C. and Taylor, H. M.},
     TITLE = {The fitting of woven cloth to surfaces},
   JOURNAL = {J.~Text. Inst. Trans.},
  FJOURNAL = {Journal of the Textile Institute Transactions},
    VOLUME = {47},
      YEAR = {1956},
    NUMBER = {9},
     PAGES = {T477--T488},
       DOI = {10.1080/19447027.1956.10750433},
       URL = {https://doi.org/10.1080/19447027.1956.10750433},
}

@article {GM-1961,
    AUTHOR = {Margulies, G.},
     TITLE = {Peterson's theorem on surfaces corresponding by parallelism.~{I}},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {12},
      YEAR = {1961},
     PAGES = {577--587},
       DOI = {10.2307/2034248},
       URL = {https://doi.org/10.2307/2034248},
}

@article {MM-rzcr,
    AUTHOR = {Marvan, Michal},
     TITLE = {Reducibility of zero curvature representations with
              application to recursion operators},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {83},
      YEAR = {2004},
    NUMBER = {1-2},
     PAGES = {39--68},
       DOI = {10.1023/B:ACAP.0000035588.67805.0b},
       URL = {https://doi.org/10.1023/B:ACAP.0000035588.67805.0b},
    EPRINT = {nlin.SI/0306006},
}

@article {MM-spp,
    AUTHOR = {Marvan, Michal},
     TITLE = {On the spectral parameter problem},
   JOURNAL = {Acta Appl. Math.},
  FJOURNAL = {Acta Applicandae Mathematicae},
    VOLUME = {109},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {239--255},
       DOI = {10.1007/s10440-009-9450-4},
       URL = {https://doi.org/10.1007/s10440-009-9450-4},
    EPRINT = {0804.2031},
}

@article {M-M-2017,
    AUTHOR = {Masson, Yannick and Monasse, Laurent},
     TITLE = {Existence of global {C}hebyshev nets on surfaces of absolute
              {G}aussian curvature less than~{$2\pi$}},
   JOURNAL = {J.~Geom.},
  FJOURNAL = {Journal of Geometry},
    VOLUME = {108},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {25--32},
       DOI = {10.1007/s00022-016-0319-1},
       URL = {https://doi.org/10.1007/s00022-016-0319-1},
}

@phdthesis {YM-2017,
    AUTHOR = {Masson, Yannick},
     TITLE = {Existence and construction of Chebyshev nets with singularities
              and application to gridshells},
      NOTE = {{U}niversit\'e Paris Est, 2017, available at \url{https://theses.hal.science/tel-01676984v1}},
}

@article {VBM-2008,
    AUTHOR = {Matveev, Vladimir B.},
     TITLE = {30 years of finite-gap integration theory},
   JOURNAL = {Philos. Trans.~R. Soc. Lond. Ser.~A Math. Phys. Eng. Sci.},
  FJOURNAL = {Philosophical Transactions of the Royal Society of London.
              Series A. Mathematical, Physical and Engineering Sciences},
    VOLUME = {366},
      YEAR = {2008},
    NUMBER = {1867},
     PAGES = {837--875},
       DOI = {10.1098/rsta.2007.2055},
       URL = {https://doi.org/10.1098/rsta.2007.2055},
}

@incollection {M-D-T-F-B,
    AUTHOR = {Montagne, N. and Douthe, C. and Tellier, X. and Fivet, C. and Baverel, O.},
     TITLE = {Voss surfaces: {A} design space for geodesic gridshells},
 BOOKTITLE = {Inspiring the Next Generation (Proc. IASS Annual Symp. 2020 and 7th Int. Conf. Spatial Structures)},
    EDITOR = {Behnejad, S. A. and Parke, G. A. R. and Samavati, O. A.},
     PAGES = {3473--3483},
 PUBLISHER = {Spatial Structures Research Centre University Surrey, UK},
      YEAR = {2021},
       DOI = {10.15126/900337},
       URL = {https://doi.org/10.15126/900337},
}

@article {M-B-2008,
    AUTHOR = {Mukherjee, Rick and Balakrishnan, Radha},
     TITLE = {Moving curves of the sine-{G}ordon equation: new links},
   JOURNAL = {Phys. Lett.~A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {372},
      YEAR = {2008},
    NUMBER = {42},
     PAGES = {6347--6362},
       DOI = {10.1016/j.physleta.2008.08.070},
       URL = {https://doi.org/10.1016/j.physleta.2008.08.070},
}

@book {APN,
    AUTHOR = {Norden, A. P.},
     TITLE = {Theory of surfaces},
 PUBLISHER = {GITTL, Moscow},
      YEAR = {1956},
     PAGES = {260},
}

@article {KMP-1866,
    AUTHOR = {Peterson, K. M.},
     TITLE = {Sur les relations et les affinit\'es entre les surfaces courbes},
   JOURNAL = {Ann. Fac. Sci. Univ. Toulouse},
  FJOURNAL = {Ann. Fac. Sci. Univ. Toulouse},
    VOLUME = {7},
      YEAR = {1905},
     PAGES = {5--43},
      NOTE = {{t}ranslated from Russian: \textit{Mat. Sb.} \textbf{1} (1866), 391--438},
}

@article {P-E-V-W,
    AUTHOR = {Pottmann, H. and Eigensatz, M. and Vaxman, A. and Wallner, J.},
     TITLE = {Architectural geometry},
   JOURNAL = {Comput. Graph.},
  FJOURNAL = {Computers \& Graphics},
    VOLUME = {47},
      YEAR = {2015},
     PAGES = {145--164},
       DOI = {10.1016/j.cag.2014.11.002},
       URL = {https://doi.org/10.1016/j.cag.2014.11.002},
}

@book {R-S,
    AUTHOR = {Rogers, C. and Schief, W. K.},
     TITLE = {B\"acklund and {D}arboux transformations. Geometry and modern applications in soliton theory},
    SERIES = {Cambridge Texts Appl. Math.},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2002},
     PAGES = {xviii+413},
       DOI = {10.1017/CBO9780511606359},
       URL = {https://doi.org/10.1017/CBO9780511606359},
}

@article {SF-C-BC-V,
    AUTHOR = {Sageman-Furnas, Andrew O. and Chern, Albert and Ben-Chen, Mirela
              and Vaxman, Amir},
     TITLE = {{C}hebyshev nets from commuting {PolyVector} fields},
   JOURNAL = {ACM Trans. Graph.},
  FJOURNAL = {ACM Transactions on Graphics},
    VOLUME = {38},
      YEAR = {2019},
    NUMBER = {6},
     PAGES = {172, 16~pages},
       DOI = {10.1145/3355089.3356564},
       URL = {https://doi.org/10.1145/3355089.3356564},
}

@article {GS,
    AUTHOR = {Sannia, G.},
     TITLE = {Geometria differenziale dei reticolati piani invariante per un
              gruppo di~collineazioni},
   JOURNAL = {Rend. Circ. Mat. Palermo},
  FJOURNAL = {Rendiconti del Circolo Matematico di Palermo},
    VOLUME = {48},
      YEAR = {1924},
     PAGES = {289--307},
       DOI = {10.1007/BF03014704},
       URL = {https://doi.org/10.1007/BF03014704},
}

@article {RS-1933,
    AUTHOR = {Sauer, Robert},
     TITLE = {Weckelige {K}urvennetze bei einer infinitesimalen
              {F}l\"achenverbiegung},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {108},
      YEAR = {1933},
    NUMBER = {1},
     PAGES = {673--693},
       DOI = {10.1007/BF01452858},
       URL = {https://doi.org/10.1007/BF01452858},
}

@book {RS-1970,
    AUTHOR = {Sauer, Robert},
     TITLE = {Differenzengeometrie},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1970},
     PAGES = {iii+234},
       DOI = {10.1007/978-3-642-86411-7},
       URL = {https://doi.org/10.1007/978-3-642-86411-7},
}

@article {WS-I,
    AUTHOR = {Scherrer, W.},
     TITLE = {Die {G}rundgleichungen der {F}l\"achentheorie.~{I}},
   JOURNAL = {Comment. Math. Helv.},
  FJOURNAL = {Commentarii Mathematici Helvetici},
    VOLUME = {29},
      YEAR = {1955},
     PAGES = {180--198},
       DOI = {10.1007/BF02564278},
       URL = {https://doi.org/10.1007/BF02564278},
}

@article {WS-II,
    AUTHOR = {Scherrer, W.},
     TITLE = {Die {G}rundgleichungen der {F}l\"achentheorie.~{II}},
   JOURNAL = {Comment. Math. Helv.},
  FJOURNAL = {Commentarii Mathematici Helvetici},
    VOLUME = {32},
      YEAR = {1957},
     PAGES = {73--84},
       DOI = {10.1007/BF02564571},
       URL = {https://doi.org/10.1007/BF02564571},
}

@article {WS-III,
    AUTHOR = {Scherrer, W.},
     TITLE = {Die {G}rundgleichungen der {F}l\"achentheorie.~{III}},
   JOURNAL = {Comment. Math. Helv.},
  FJOURNAL = {Commentarii Mathematici Helvetici},
    VOLUME = {37},
      YEAR = {1962},
     PAGES = {177--197},
       DOI = {10.1007/BF02566971},
       URL = {https://doi.org/10.1007/BF02566971},
}

@article {S-R-1999,
    AUTHOR = {Schief, W. K. and Rogers, C.},
     TITLE = {Binormal motion of curves of constant curvature and torsion.
              {G}eneration of soliton surfaces},
   JOURNAL = {R.~Soc. Lond. Proc. Ser.~A Math. Phys. Eng. Sci.},
  FJOURNAL = {The Royal Society of London. Proceedings. Series A.
              Mathematical, Physical and Engineering Sciences},
    VOLUME = {455},
      YEAR = {1999},
    NUMBER = {1988},
     PAGES = {3163--3188},
       DOI = {10.1098/rspa.1999.0445},
       URL = {https://doi.org/10.1098/rspa.1999.0445},
}

@article {WKS-2003,
    AUTHOR = {Schief, W. K.},
     TITLE = {On the integrability of {B}ertrand curves and {R}azzaboni
              surfaces},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {45},
      YEAR = {2003},
    NUMBER = {1-2},
     PAGES = {130--150},
       DOI = {10.1016/S0393-0440(02)00130-4},
       URL = {https://doi.org/10.1016/S0393-0440(02)00130-4},
}

@article {WKS-2007,
    AUTHOR = {Schief, W. K.},
     TITLE = {Discrete {C}hebyshev nets and a~universal permutability
              theorem},
   JOURNAL = {J.~Phys.~A},
  FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
    VOLUME = {40},
      YEAR = {2007},
    NUMBER = {18},
     PAGES = {4775--4801},
       DOI = {10.1088/1751-8113/40/18/007},
       URL = {https://doi.org/10.1088/1751-8113/40/18/007},
}

@article {MS-1904,
    AUTHOR = {Servant, M.},
     TITLE = {Sur l'habillage des surfaces},
   JOURNAL = {C.~R.~Acad. Sci.},
  FJOURNAL = {Comptes rendus de l'Acad\'emie des Sciences},
    VOLUME = {137},
      YEAR = {1903},
     PAGES = {112--115},
}

@article {HJS,
    AUTHOR = {Shin, H. J.},
     TITLE = {Lund--{R}egge vortex strings in terms of {W}eierstrass elliptic
              functions},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {624},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {431--451},
       DOI = {10.1016/S0550-3213(01)00645-9},
       URL = {https://doi.org/10.1016/S0550-3213(01)00645-9},
}

@book {VIS,
    AUTHOR = {Shulikovsky, V. I.},
     TITLE = {Classical differential geometry},
 PUBLISHER = {GIFML, Moscow},
      YEAR = {1963},
}

@book {Spi-III,
    AUTHOR = {Spivak, Michael},
     TITLE = {A~comprehensive introduction to differential geometry. {V}ol.~{III}},
 PUBLISHER = {Publish or Perish, Inc., Boston, MA},
      YEAR = {1975},
     PAGES = {ix+474},
}

@incollection {Sym,
    AUTHOR = {Sym, Antoni},
     TITLE = {Soliton surfaces and their applications (soliton geometry from
              spectral problems)},
 BOOKTITLE = {Geometric Aspects of the {E}instein Equations and Integrable
              Systems ({S}cheveningen, 1984)},
    SERIES = {Lecture Notes in Phys.},
    VOLUME = {239},
     PAGES = {154--231},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1985},
       DOI = {10.1007/3-540-16039-6\_6},
       URL = {https://doi.org/10.1007/3-540-16039-6_6},
}

@article {XT-2022,
    AUTHOR = {Tellier, Xavier},
     TITLE = {Bundling elastic gridshells with alignable nets. Part~{I}:
              {A}nalytical approach},
   JOURNAL = {Autom. Constr.},
  FJOURNAL = {Automation in Construction},
    VOLUME = {141},
      YEAR = {2022},
     PAGES = {104291, 36~pages},
       DOI = {10.1016/j.autcon.2022.104291},
       URL = {https://doi.org/10.1016/j.autcon.2022.104291},
}

@article {CT-1988,
    AUTHOR = {Tian, Chou},
     TITLE = {Foliation on a~surface of constant curvature and some
              nonlinear evolution equations},
   JOURNAL = {Chinese Ann. Math. Ser.~B},
  FJOURNAL = {Chinese Annals of Mathematics. Series B. Shuxue Niankan. B Ji},
    VOLUME = {9},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {118--122},
}

@article {MT-2017,
    AUTHOR = {Toda, Magdalena},
     TITLE = {On a~duality property of isothermic surfaces},
   JOURNAL = {JP J.~Geom. Topol.},
  FJOURNAL = {JP Journal of Geometry and Topology},
    VOLUME = {20},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {85--90},
       DOI = {10.17654/GT020010085},
       URL = {https://doi.org/10.17654/GT020010085},
}

@article {V-B-2010,
    AUTHOR = {Vashpanova, T. Yu. and Bezkorovaynaya, L. L.},
     TITLE = {LGT-network of a~surface and its properties},
   JOURNAL = {Visn. Kyiv. Univ. im. Tarasa Shevchenka, Ser. Fiz.-Mat. Nauk},
  FJOURNAL = {Bulletin of Taras Shevchenko National University of Kyiv. Series:
              Physics and Mathematics},
    VOLUME = {2010},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {no.~2, 7--11},
}

@article {Vax-2016,
    AUTHOR = {Vaxman, Amir and Campen, Marcel and Diamanti, Olga and
              Panozzo, Daniele and Bommes, David and Hildebrandt, Klaus and
              Ben-Chen, Mirela},
     TITLE = {Directional field synthesis, design, and processing},
   JOURNAL = {Comput. Graph. Forum},
  FJOURNAL = {Computer Graphics Forum},
    VOLUME = {35},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {545--572},
       DOI = {10.1111/cgf.12864},
       URL = {https://doi.org/10.1111/cgf.12864},
}

@article {AV-1869,
    AUTHOR = {Voss, A.},
     TITLE = {Ueber ein neues {P}rincip der {A}bbildung krummer
              {O}berfl\"achen},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {19},
      YEAR = {1881},
    NUMBER = {1},
     PAGES = {1--26},
       DOI = {10.1007/BF01447291},
       URL = {https://doi.org/10.1007/BF01447291},
}

@article {W-P-2022,
    AUTHOR = {Wang, Hui and Pottmann, Helmut},
     TITLE = {Characteristic parameterizations of surfaces with a~constant
              ratio of principal curvatures},
   JOURNAL = {Comput. Aided Geom. Design},
  FJOURNAL = {Computer Aided Geometric Design},
    VOLUME = {93},
      YEAR = {2022},
     PAGES = {102074, 23~pages},
       DOI = {10.1016/j.cagd.2022.102074},
       URL = {https://doi.org/10.1016/j.cagd.2022.102074},
}

@article {CEW,
    AUTHOR = {Weatherburn, C. E.},
     TITLE = {On {L}evi-{C}ivita's theory of parallelism},
   JOURNAL = {Bull. Amer. Math. Soc.},
  FJOURNAL = {Bulletin of the American Mathematical Society},
    VOLUME = {34},
      YEAR = {1928},
    NUMBER = {5},
     PAGES = {585--590},
       DOI = {10.1090/S0002-9904-1928-04629-3},
       URL = {https://doi.org/10.1090/S0002-9904-1928-04629-3},
}

@article {KHW-1940,
    AUTHOR = {Weise, Karl Heinrich},
     TITLE = {Invariante {C}harakterisierung von {K}urvennetzen},
   JOURNAL = {Math.~Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {46},
      YEAR = {1940},
     PAGES = {665--691},
       DOI = {10.1007/BF01181462},
       URL = {https://doi.org/10.1007/BF01181462},
}

@article {JKW,
    AUTHOR = {Whittemore, J. K.},
     TITLE = {Total geodesic curvature and geodesic torsion},
   JOURNAL = {Bull. Amer. Math. Soc.},
  FJOURNAL = {Bulletin of the American Mathematical Society},
    VOLUME = {29},
      YEAR = {1923},
    NUMBER = {2},
     PAGES = {51--54},
       DOI = {10.1090/S0002-9904-1923-03659-8},
       URL = {https://doi.org/10.1090/S0002-9904-1923-03659-8},
}

@article {Wolf,
    AUTHOR = {Wolf, Thomas},
     TITLE = {A~comparison of four approaches to the calculation of
              conservation laws},
   JOURNAL = {European J.~Appl. Math.},
  FJOURNAL = {European Journal of Applied Mathematics},
    VOLUME = {13},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {129--152},
       DOI = {10.1017/S0956792501004715},
       URL = {https://doi.org/10.1017/S0956792501004715},
}

@article {Z-S-1974,
    AUTHOR = {Zakharov, V. E. and Shabat, A. B.},
     TITLE = {Integration of nonlinear equations of mathematical physics
              by the method of inverse scattering.~{II}},
   JOURNAL = {Funct. Anal. Appl.},
  FJOURNAL = {Functional Analysis and Its Applications},
    VOLUME = {13},
      YEAR = {1979},
    NUMBER = {3},
     PAGES = {166--174},
       DOI = {10.1007/BF01077483},
       URL = {https://doi.org/10.1007/BF01077483},
}
