The Randers metrics of weakly isotropic scalar curvature

TL;DR

This paper investigates Randers metrics with weakly isotropic scalar curvature, establishing conditions under which they exhibit isotropic S-curvature and classifying conformally flat cases as Minkowskian or Riemannian.

Contribution

It proves that Randers metrics with weakly isotropic scalar curvature must have isotropic S-curvature and classifies conformally flat cases, advancing understanding of their geometric properties.

Findings

Randers metrics of weakly isotropic scalar curvature have isotropic S-curvature.

Conformally flat Randers metrics with this property are either Minkowskian or Riemannian.

The paper provides new classifications for these geometric structures.

Abstract

In this paper, we study the Randers metrics of weakly isotropic scalar curvature. We prove that a Randers metric of weakly isotropic scalar curvature must be of isotropic $S$-curvature. Further, we prove that a conformally flat Randers metric of weakly isotropic scalar curvature is either Minkowskian or Riemannian.