Non-contractible closed geodesics on compact Finsler space forms without self-intersections
Year: 2024
Type: preprint
Abstract: Let $M=S^n/ Γ$ and $h \in π_1(M)$ be a non-trivial element of finite order $p$, where the integers $n, p\geq2$ 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 $\mathbb{R}P^2$ 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 \[ F^2 <(\frac{λ+1}λ)^2 g_0 \;\; \text{ and } \;\; (\fracλ{λ+1})^2 < K \leq 1 \text{ for $n$ is odd or }\; 0
Source: arXiv (Cornell University)
Author: Wang, Yuchen
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390573251