ON THE SECTIONAL CURVATURE OF THE HOMOGENEOUS CONNECTION ON FINSLER MANIFOLD

摘要

Using the notations of Fr?licher-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 X e TTM, 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 f ∈ C~∞(M) such that the curvature R of Γ satisfies R = fi_C? ^ J， where Ω = dd_JE，C the Liouville vector field and J the almost tangent structure [8].