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arXiv · 1804.08452

Two closed geodesics on compact bumpy Finsler manifolds

Wei Wang
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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}.

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Wei Wang. 2018-04-20. Two closed geodesics on compact bumpy Finsler manifolds. https://arxiv.org/abs/1804.08452

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