On isotropic Berwald scalar curvature

Abstract

In this paper, we establish a closer relation between the Berwald scalar curvature and the [Formula: see text]-curvature. In fact, we prove that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic [Formula: see text]-curvature. For Finsler metrics of scalar flag curvature and of weakly isotropic [Formula: see text]-curvature, they have almost isotropic [Formula: see text]-curvature if and only if the flag curvature is weakly isotropic.