Two elliptic closed geodesics on positively curved Finsler spheres

2015/04/30 by Huagui Duan
Mathematics · #math.DG

paper · pdf · doi:10.1016/j.jde.2016.02.025

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

arxiv created 2015/07/10 · arxiv updated 2016/02/26

Abstract

In this paper, we prove that for every Finsler n-dimensional sphere (Sⁿ,F) with reversibility \lm and flag curvature K satisfying ((\lm)/(1+\lm))²<K≤ 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^√(-1)þ with þ being an irrational multiple of π.

Citations

• Existence of closed geodesics on Finsler n-spheres

Cited by

• On the multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics