Some properties of Sasaki metric on the tangent bundle of Finsler manifolds

Let (m,f) be a finsler manifold and g be the sasaki-finsler metric on tm∼. in this paper, we investigate some properties of sasaki-finsler metric which is pure with respect to some paracomplex structures on tm∼. also, we show that the curvature tensor field of the levi-civita connection on (tm,g) is recurrent or pseudo symmetric if and only if (m,f) is locally eulidean or locally minkowski space.