Two short closed geodesics on a sphere of odd dimension

2022/03/15 by Hans–Bert Rademacher, Rademacher, Hans-Bert
Mathematics · Physics and Astronomy · #53C22 #58E10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.07896

openalex publication_date 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for an open and dense set non-reversible Finsler metrics on a sphere of odd dimension n=2m-1 ≥ 3 there is a second closed geodesic with Morse index ≤ 4(m+2)(m-1)+2.

Related

• The second closed geodesic on Finsler spheres of dimension n>2
• Multiple closed geodesics on Finsler 3-dimensional sphere
• The existence of two closed geodesics on every Finsler 2-sphere
• Bumpy metrics on spheres and minimal index growth
• The index growth and multiplicity of closed geodesics