On some m-th root metrics

Abstract

The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the -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.

Keywords

• scalar curvature
• weakly isotropic scalar curvature
• $ m $-th root finsler metrics
• locally conformally flat
• cubic metrics