Non-contractible closed geodesics on compact Finsler space forms without self-intersections

2024/01/01 by Yuchen Wang, Wang, Yuchen
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Combinatorics #Computer science #Contractible space #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geodesic #Mathematical analysis #Mathematics #Pure mathematics #Space (punctuation) #Topology (electrical circuits)

paper · pdf · doi:10.48550/arxiv.2401.00946

openalex publication_date 2024/01/01 · openalex created_date 2024/01/04 · openalex updated_date 2026/07/28

Abstract

Let M=Sⁿ/ Γ and h ∈ π₁(M) be a non-trivial element of finite order p, where the integers n, p≥2 and Γ is a finite abelian group which acts on the sphere freely and isometrically, therefore M is diffeomorphic to a compact space form which is typical a non-simply connected manifold. We prove there exist at least two non-contractible closed geodesics on ℝP² and obtain the upper bounds on their lengths. Moreover, we prove there exist at least n prime non-contractible simple closed geodesics on (M,F) of prescribed class [h], provided \[ F² <(\fracλ+1λ)² g₀ and (\fracλλ+1)² < K ≤ 1 for n is odd or 0

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