On the average indices of closed geodesics on positively curved Finsler spheres

2008/11/29 by Wei Wang, Wang, Wei · 2 citations
Mathematics · Physics and Astronomy · #53C22 #53C60 #58E10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C22 #msc:53C60 #msc:58E10

paper · pdf · doi:10.48550/arxiv.0812.0039

18 pages

arxiv created 2008/11/29 · openalex publication_date 2008/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that on every Finsler n-sphere (Sⁿ, F) for n≥ 6 with reversibility λ and flag curvature K satisfying (\fracλλ+1)²<K≤ 1, either there exist infinitely many prime closed geodesics or there exist [(n)/(2)]-2 closed geodesics possessing irrational average indices. If in addition the metric is bumpy, then there exist n-3 closed geodesics possessing irrational average indices provided the number of closed geodesics is finite.

Cited by

• Multiple closed geodesics on positively curved Finsler manifolds
• Non-hyperbolic closed geodesics on positively curved Finsler spheres

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