Two closed geodesics on compact bumpy Finsler manifolds

2018/04/20 by Wang, Wei
#53C22 #58E05 #58E10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.08452

Abstract

In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler n-manifold with finite fundamental group and n≥ 2. Thus generically there are at least two closed geodesics on compact Finsler manifolds with finite fundamental group. Furthermore, there are at least two closed geodesics on any compact Finsler 2-manifold, and this lower bound is achieved by the Katok 2-sphere (S², F) and 2-real projective space (S²/\Z₂, F), cf. \citeKat.

Related

• The second closed geodesic on Finsler spheres of dimension n>2
• The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form S²ⁿ⁺¹/ Γ
• The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form
• The existence of two closed geodesics on every Finsler 2-sphere
• Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics