Two elliptic closed geodesics on positively curved Finsler spheres

Abstract

In this paper, we prove that for every Finsler $n$-dimensional sphere $(S^n,F)$ with reversibility $\lm$ and flag curvature $K$ satisfying $\left(\frac{\lm}{1+\lm}\right)^2<K\le 1$, either there exist infinitely many closed geodesics, or there exist at least two elliptic closed geodesics and each linearized Poincaré map has at least one eigenvalue of the form $e^{\sqrt{-1}þ}$ with $þ$ being an irrational multiple of $\pi$.

12 pages, submitted. arXiv admin note: text overlap with arXiv:0909.3566 by other authors

References in corpus (3)

• Multiple closed geodesics on bumpy Finsler $n$-spheres
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
• Closed geodesics on positively curved Finsler spheres

Cited by in corpus (3)

• Non-hyperbolic closed geodesics on positively curved Finsler spheres
• Finsler spheres with constant flag curvature and finite orbits of prime closed geodesics
• The number of geometrically distinct reversible closed geodesics on a Finsler sphere with $K\equiv 1$