Address: Department of Mathematics, Minjiang University Fuzhou, Fujiang, 350108, China
E-mail: bingyewu@yahoo.com.cn
Abstract: In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.
AMSclassification: primary 53C60; secondary 53B40.
Keywords: Finsler manifold, Landsberg manifold, scalar flag curvature, sectional flag curvature, Cartan tensor.