Using the notations of Frölicher-Nijenhuis [1, 4], and results of [2, 3, 11], we consider a Finsler manifold (M, E) and the Grifone- Ehersmann connection Γ [8]. We define the sectional curvature k(X) of tangent vector  and prove the Schur’s theorem on the Finsler manifold. Also, we prove that the sectional curvature is constant if and only if there exists a function  such that the curvature R of Γ satisfies  where  C the Liouville vector field and J the almost tangent structure [8].

Finsler manifold, homogeneous connection, sectional curvature, spray, Schur’s theorem.