Let M be a smooth manifold with Finsler metric F, and let TM° be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM°,G) and study some of their geometric properties. Next we use this approach to obtain new characterizations of Finsler manifolds with positive constant curvature.
