Gromov hyperbolicity of negatively curved Finsler manifolds

Let ( M, F) be a closed C-infinity Finsler manifold. The lift of the Finsler metric F to the universal covering space defines an asymmetric distance (d) over tilde on (M) over tilde. It is well-known that the classical comparison theorem of Aleksandrov does not exist in the Finsler setting. Therefore, it is necessary to introduce new Finsler tools for the study of the asymmetric metric space ( (M) over tilde, (d) over tilde). In this paper, by using the geometric flip map and the unstable-stable angle introduced in [2], we prove that if ( M, F) is a closed Finsler manifold of negative flag curvature, then ((M) over tilde, (d) over tilde) is an asymmetric delta-hyperbolic space in the sense of Gromov.