Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs
Differential Geometry
2023-07-03 v1 Dynamical Systems
Abstract
We prove that if the geodesic flow on a surface has an integral, fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case corresponding to constant gaussian curvature. We give also a geometric criterion for existence of fractional-linear integrals: such integral exists if and only if the surface carries a geodesic 4-web with constant cross-ratio of the four directions tangent to the web leaves.
Keywords
Cite
@article{arxiv.2306.17540,
title = {Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs},
author = {Sergey I. Agafonov and Thaís G. P. Alves},
journal= {arXiv preprint arXiv:2306.17540},
year = {2023}
}
Comments
15 pages