Elliptic closed geodesics on non-negatively curved Finsler manifolds

Abstract

In this paper, we prove that if a compact simply-connected manifold $(M,F)$ with a bumpy irreversible Finsler metric $F$ whose flag curvature $K$ satisfies $K\ge 0$ and H^*(M;\Q)\cong T_{d,n+1}(x) for some $d\in2\N$ and $n\in\N$ carries exactly $\frac{dn(n+1)}{2}$ (the number of closed geodesics in Katok's example) closed geodesics, then there are at least $2$ irrationally elliptic closed geodesics on $(M, F)$.