Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres

2007/05/30 by Huagui Duan, Duan, Huagui, Yiming Long +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fibroblast Growth Factor Research #Geometric Analysis and Curvature Flows #math.DG

paper · pdf · doi:10.48550/arxiv.0705.4326

17 pages. Some modifications have been made. accepted by Calc. Var. & PDEs

openalex publication_date 2007/05/30 · arxiv created 2007/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every \Q-homological Finsler 3-sphere (M,F) with a bumpy and irreversible metric F, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.

Citations

• Existence of closed geodesics on positively curved Finsler manifolds

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• Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics
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• Multiplicity and stability of closed geodesics on positively curved Finsler 4-spheres