Existence of closed geodesics on Finsler $n$-spheres

Details Existence of closed geodesics on Finsler $n$-spheres Existence of closed geodesics on Finsler $n$-spheres

2009-09-19

arxiv.org/abs/0909.3566v1

Mathematics

Differential Geometry

12 pages

Scientific paper

In this paper, we prove that on every Finsler $n$-sphere $(S^n, F)$ with reversibility $\lambda$ satisfying $F^2<(\frac{\lambda+1}{\lambda})^2g_0$ and $l(S^n, F)\ge \pi(1+\frac{1}{\lambda})$, there always exist at least $n$ prime closed geodesics without self-intersections, where $g_0$ is the standard Riemannian metric on $S^n$ with constant curvature 1 and $l(S^n, F)$ is the length of a shortest geodesic loop on $(S^n, F)$. We also study the stability of these closed geodesics.

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