Existence results for closed Finsler geodesics via spherical complexities
Differential Geometry
2021-05-05 v2 Algebraic Topology
Geometric Topology
Abstract
We apply topological methods and a Lusternik-Schnirelmann-type approach to prove existence results for closed geodesics of Finsler metrics on spheres and projective spaces. The main tool in the proofs are spherical complexities, which have been introduced in earlier work of the author. Using them, we show how pinching conditions and inequalities between a Finsler metric and a globally symmetric metric yield the existence of multiple closed geodesics as well as upper bounds on their lengths.
Keywords
Cite
@article{arxiv.2003.07259,
title = {Existence results for closed Finsler geodesics via spherical complexities},
author = {Stephan Mescher},
journal= {arXiv preprint arXiv:2003.07259},
year = {2021}
}
Comments
13 pages, revised version, to appear in Calc. Var