Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics

2022/01/26 by Huagui Duan, Dong Xie, Duan, Huagui +1
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.10975

Abstract

Let M be a compact simply connected manifold satisfying H^*(M;Q)≅ T_d,n+1(x) for integers d≥ 2 and n≥ 1. If all prime closed geodesics on (M,F) with an irreversible bumpy Finsler metric F are elliptic, either there exist exactly (dn(n+1))/(2) (when d≥ 2 is even) or (d+1) (when d≥ 3 is odd) distinct closed geodesics, or there exist infinitely many distinct closed geodesics.

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