On some $ m $-th root metrics

The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the $ m $-th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish. Further, we prove that a locally conformally flat cubic Finsler metric with weakly isotropic scalar curvature must be locally Minkowskian.