On $m$-th root metrics of isotropic projective Ricci curvature
نویسندگان
1 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran
2 Department of Mathematics, Istanbul Bilgi University, 34060, Eski Silahtaraga Elektrik Santrali, Kazim Karabekir Cad. No: 2/13 Eyupsultan, Istanbul, Turkey
3 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran
doi
10.22060/ajmc.2022.21830.1113چکیده
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 introduced the idea of weakly isotropic projective Ricci curvature in \cite{GRS21Square}. 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.
