Webs of positive rank with prescribed geometry

• Grant number: 22/12813-5
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2023
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Serguei Agafonov
• Grantee: Serguei Agafonov
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• City of the host institution: São José do Rio Preto

Abstract

This project proposes study of the web rank problem with the prescribed geometry of leaves. Will be investigated the following web types:1) geodesic webs in Riemannian manifolds of dimension three, 2) planar hexagonal 3-webs of circles, and 3) planar webs of conics with positive rank. Geodesic webs to be considered are constructed from 2 first integrals of geodesic flow, homogeneous and polynomial in velocity, the webs leaves being integral curves of the directions on which both integrals vanish. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AGAFONOV, SERGEY I.; ALVES, THAIS G. P.. Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs. ADVANCES IN GEOMETRY, v. 24, n. 2, p. 11-pg., 2024-04-25. (22/12813-5)

AGAFONOV, SERGEY I.. Integrable geodesic flow in 3D and webs of maximal rank. ANALYSIS AND MATHEMATICAL PHYSICS, v. 14, n. 6, p. 21-pg., 2024-12-01. (22/12813-5)

AGAFONOV, SERGEY I.. Hexagonal Circular 3-Webs with Reducible Polar Curves of Degree Three. Symmetry Integrability and Geometry-Methods and Applications, v. 21, p. 31-pg., 2025-01-01. (22/12813-5)