On m-th root metrics of isotropic projective Ricci curvature

Abstract

The Ricci curvature is introduced by spray on Mn. Sprays are deformed to projective sprays with a volume form dV on Mn. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays. With this paper, we use the new notion that is called weakly isotropic projective Ricci curvature. We have introduced the idea of weakly isotropic projective Ricci curvature in [3]. Then we study and characterize m-th root metrics of weakly isotropic projective Ricci curvature. We obtain that every m-th root metric of weakly isotropic projective Ricci curvature is projectively Ricci-flat. © 2023, Amirkabir University of Technology. All rights reserved.