Some rigidity theorems for Finsler manifolds of sectional flag curvature

Bing Ye Wu

Address: Department of Mathematics, Minjiang University Fuzhou, Fujiang, 350108, China


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.