Year: 2026
Type: preprint
Abstract: Let $M = S^{2n+1}/Γ$ be a manifold diffeomorphic to a compact space form, endowed with a bumpy Finsler metric $F$. In this paper, we prove that there exist at least $n+3$ contractible minimal closed geodesics on $M$, assuming that all contractible minimal closed geodesics have non-zero Morse indices. Here, a contractible closed geodesic is called minimal if it is not an iteration of any other contractible closed geodesic. In particular, this confirms the generalized Anosov-Katok conjecture for the bumpy quotient manifold $(S^3/Γ, F)$ under the non-zero Morse index assumption.
Source: arXiv (Cornell University)
Authors: Liu, Hui, Qi, Linxinzi
Institution: Wuhan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4349787602
OpenAlex ID: W7223105577