Finsler geometry and natural foliations on the tangent bundle

A new approach for the study of geometry of Finsler manifolds is proposed. Let Fm = (M, F) be an m-dimensional Finsler manifold and G be the Sasaki-Finsler metric on T M0 = T M0}. We exploit many natural foliations of T M0 G) by showing that their geometry is closely related to that of the Finsler manifold itself. In particular, we use this approach to obtain new characterizations of Finsler manifolds with positive constant curvature.