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arXiv · 1508.05577

Non-hyperbolic closed geodesics on positively curved Finsler spheres

Huagui Duan
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Abstract

In this paper, we prove that for every Finsler $n$-dimensional sphere $(S^n,F), n\ge 3$ with reversibility $λ$ and flag curvature $K$ satisfying $\left(\fracλ{1+λ}\right)^2<K\le 1$, there exist at least three distinct closed geodesics and at least two of them are elliptic if the number of prime closed geodesics is finite. When $n\ge 6$, these three distinct closed geodesics are non-hyperbolic.

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Huagui Duan. 2015-08-23. Non-hyperbolic closed geodesics on positively curved Finsler spheres. https://doi.org/10.1016/j.jfa.2015.08.016

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