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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2025 Volume 21, 043, 31 pp. (Mi sigma2160)

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

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.

Keywords: circular hexagonal 3-webs.

MSC: 53A60

Received: November 18, 2023; in final form June 4, 2025; Published online June 13, 2025

Language: English

DOI: 10.3842/SIGMA.2025.043


ArXiv: 2306.11707


© Steklov Math. Inst. of RAS, 2025