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

SIGMA 21 (2025), 043, 31 pages      arXiv:2306.11707      https://doi.org/10.3842/SIGMA.2025.043

Hexagonal Circular 3-Webs with Reducible Polar Curves of Degree Three

Sergey I. Agafonov
Department of Mathematics, São Paulo State University-UNESP, São José do Rio Preto, Brazil

Received November 18, 2023, in final form June 04, 2025; Published online June 13, 2025

Abstract
The paper reports the progress with the classical problem, posed by Blaschke and Bol in 1938. We present new examples and new classifications of natural classes of hexagonal circular 3-webs. The main results is the classification of hexagonal circular 3-webs with reducible polar curves of degree 3 and description of hexagonal circular 3-webs admitting a one-parameter Möbius symmetry.

Key words: circular hexagonal 3-webs.

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