Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 069, 8 pages      arXiv:2502.19520      https://doi.org/10.3842/SIGMA.2025.069

Curves on Endo-Pajitnov Manifolds

Cristian Ciulică
Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei Str., 010014 Bucharest, Romania

Received February 28, 2025, in final form August 06, 2025; Published online August 13, 2025

Abstract
Endo-Pajitnov manifolds are generalizations to higher dimensions of the Inoue surfaces $S^M$. We study the existence of complex submanifolds in Endo-Pajitnov manifolds. We identify a class of these manifolds that do contain compact complex submanifolds and establish an algebraic condition under which an Endo-Pajitnov manifold contains no compact complex curves.

Key words: Inoue surface; Oeljeklaus-Toma manifold; Endo-Pajitnov manifold; foliation.

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References

  1. Brunella M., A characterization of Inoue surfaces, Comment. Math. Helv. 88 (2013), 859-874, arXiv:1011.2035.
  2. Bryant R.L., An introduction to Lie groups and symplectic geometry, Duke University, Durham, NC, 1991, available at https://sites.math.duke.edu/ bryant/ParkCityLectures.pdf.
  3. Chiose I., Toma M., On compact complex surfaces of Kähler rank one, Amer. J. Math. 135 (2013), 851-860, arXiv:1010.2591.
  4. Ciulică C., Otiman A., Stanciu M., Special non-Kähler metrics on Endo-Pajitnov manifolds, Ann. Mat. Pura Appl. 204 (2025), 1425-1441, arXiv:2403.15618.
  5. Endo H., Pajitnov A., On generalized Inoue manifolds, Proc. Int. Geom. Cent. 13 (2020), 24-39, arXiv:1903.08030.
  6. Huybrechts D., Complex geometry: An introduction, Universitext, Springer, Berlin, 2005.
  7. Inoue M., On surfaces of class ${\rm VII}_{0}$, Invent. Math. 24 (1974), 269-310.
  8. Oeljeklaus K., Toma M., Non-Kähler compact complex manifolds associated to number fields, Ann. Inst. Fourier (Grenoble) 55 (2005), 161-171.
  9. Ornea L., Verbitsky M., Oeljeklaus-Toma manifolds admitting no complex subvarieties, Math. Res. Lett. 18 (2011), 747-754, arXiv:1009.1101.
  10. Verbitskaya S.M., Surfaces on Oeljeklaus-Toma manifolds, arXiv:1306.2456.
  11. Verbitskaya S.M., Curves on Oeljeklaus-Toma manifolds, Funct. Anal. Appl. 48 (2014), 223-226.

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