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arXiv · 1803.08350

Multiple closed geodesics on positively curved Finsler manifolds

Wei Wang
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Abstract

In this paper, we prove that on every Finsler manifold $(M,\,F)$ with reversibility $\lambda$ and flag curvature $K$ satisfying $\left(\frac{\lambda}{\lambda+1}\right)^2<K\le 1$, there exist $[\frac{\dim M+1}{2}]$ closed geodesics. If the number of closed geodesics is finite, then there exist $[\frac{\dim M}{2}]$ non-hyperbolic closed geodesics. Moreover, there are 3 closed geodesics on $(M,\,F)$ satisfying the above pinching condition when $\dim M=3$.

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Wei Wang. 2018-03-21. Multiple closed geodesics on positively curved Finsler manifolds. https://arxiv.org/abs/1803.08350

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