ON THE SECTIONAL CURVATURE OF THE HOMOGENEOUS CONNECTION ON FINSLER MANIFOLD
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.