In this paper, we introduce a Riemannian metric and a family of framed f-structures on the slit tangent bundle of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if , (ii) the Jacobi operator is zero or commuting if and only if (M, F) have the zero flag curvature.
