Multiplicity of non-contractible closed geodesics on Finsler compact space forms

2022/02/21 by Hui Liu, Yuchen Wang, Liu, Hui +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #53C22 #58E05 #58E10 #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2202.10004

openalex publication_date 2022/02/21 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let M=Sⁿ/ Γ and h be a nontrivial element of finite order p in π₁(M), where the integer n, p≥2, Γ is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that for every irreversible Finsler compact space form (M,F) with reversibility λ and flag curvature K satisfying (4p²)/((p+1)²) (\fracλλ+1 )² lt; K ≤ 1, λlt; (p+1)/(p-1), there exist at least n-1 non-contractible closed geodesics of class [h]. In addition, if the metric F is bumpy and \[ ((4p)/(2p+1))² (\fracλλ+1)² < K ≤ 1, λ

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