The Randers metrics of weakly isotropic scalar curvature

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.