On isotropic Berwald scalar curvature

TL;DR

This paper explores the relationship between Berwald scalar curvature and S-curvature in Finsler geometry, establishing conditions under which these curvatures are isotropic or weakly isotropic, thus deepening understanding of curvature properties.

Contribution

It proves that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic S-curvature, clarifying their equivalence.

Findings

Equivalence between isotropic Berwald scalar curvature and weakly isotropic S-curvature.

Characterization of almost isotropic S-curvature in scalar flag curvature metrics.

Deeper insight into curvature conditions in Finsler geometry.

Abstract

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