On m-th root metrics of isotropic projective Ricci curvature

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran

2 Faculty of Science, Urmia University, Urmia, Iran

3 Department of Mathematics, Istanbul Bilgi University, 34060, Eski Silahtaraga Elektrik Santrali Kazim Karabekir Cad. No: 2/13 Eyupsultan, Istanbul, Turkey

Abstract

The Ricci curvature is introduced by spray on M^n. Sprays are deformed

to projective sprays with a volume form dV on M^n. 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 intro-

duced 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.

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