Multiple closed geodesics on positively curved Finsler manifolds

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 $\dim M=3$.

arXiv comment36 pages. arXiv admin note: text overlap with arXiv:0812.0039, arXiv:0705.4190, arXiv:1112.5234; text overlap with arXiv:1405.4057, arXiv:1504.07007, arXiv:1504.00245, arXiv:1309.3398 by other authors

References in corpus (3)

• Multiple closed geodesics on bumpy Finsler $n$-spheres
• Multiplicity of Closed Reeb Orbits on Prequantization Bundles
• The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form

Cited by in corpus (1)

• Closed geodesics on positively curved spheres $S^n$ with Finsler metric induced by $(\mathbb{R}{P}^n,F)$