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In this paper, we study the Randers metrics of weakly isotropic scalarcurvature. We prove that a Randers metric of weakly isotropic scalar curvaturemust be of isotropic $S$-curvature. Further, we prove that a conformally flatRanders metric of weakly isotropic scalar curvature is either Minkowskian orRiemannian.

The Randers metrics of weakly isotropic scalar curvature