Webs of positive rank with prescribed geometry

• Grant number: 22/12813-5
• Support Opportunities: Regular Research Grants
• Duration: March 01, 2023 - 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

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)