Two closed geodesics on compact bumpy Finsler manifolds

Wei Wang

Two closed geodesics on compact bumpy Finsler manifolds

Differential Geometry 2025-06-06 v2

Authors: Wei Wang

Abstract

In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$ -manifold with finite fundamental group and $n\ge 2$ . Thus generically there are at least two closed geodesics on compact Finsler manifolds with finite fundamental group. Furthermore, there are at least two closed geodesics on any compact Finsler $2$ -manifold, and this lower bound is achieved by the Katok 2-sphere $(S^2, F)$ and 2-real projective space $(S^2/\Z_2, F)$ , cf. \cite{Kat}.

Keywords

finsler geometry geodesics and riemannian geometry

Cite

@article{arxiv.1804.08452,
  title  = {Two closed geodesics on compact bumpy Finsler manifolds},
  author = {Wei Wang},
  journal= {arXiv preprint arXiv:1804.08452},
  year   = {2025}
}

Comments

10 pages. arXiv admin note: substantial text overlap with arXiv:1803.08350; text overlap with arXiv:1504.07007 by other authors

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