The second closed geodesic on Finsler manifolds with ${\mathbb{Z}}_2$ fundamental group

Huagui Duan, Hui Liu, Wei Wang

Let $(M,F)$ be a compact bumpy Finsler manifold with ${\pi }_1(M)={\mathbb{Z}}_2$, we prove that there exist at least two distinct non-contractible closed geodesics on $(M,F)$.