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Volume 19, Issue 3

# Multiple Closed Geodesics on Positively Curved Finsler Manifolds

Wei Wang
Published Online: 2019-04-09 | DOI: https://doi.org/10.1515/ans-2019-2043

## Abstract

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

MSC 2010: 53C22; 53C60; 58E10

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Revised: 2019-03-13

Accepted: 2019-03-14

Published Online: 2019-04-09

Published in Print: 2019-08-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11222105

Award identifier / Grant number: 11431001

The author was partially supported by the National Natural Science Foundation of China, Grant No. 11222105 and No. 11431001.

Citation Information: Advanced Nonlinear Studies, Volume 19, Issue 3, Pages 495–518, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365,

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