On the Flag Curvature of Finsler Manifolds

Abstract

In this paper, firstly we prove that all R-quadratic manifolds with nonzero scalar flag curvature must be Riemannian spaces with constant sectional curvature. We introduce the definition of the scalar curvature condition. We can prove that if (M, F) is a Randers space with constant flag curvature K satisfying the scaler curvature condition, then (M, F) is either a locally Minkowskian space with $K=0$ or a Riemannian space with constant sectional curvature $K\ne 0$.

Keywords

R-quadratic manifolds / Randers spaces / Scalar curvature condition / Flag curvature / 53C60 / 53B40

Funding

National Natural Science Foundation of China(11871405)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature