Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24494220230301On m-th root metrics of isotropic projective Ricci curvature123128498410.22060/ajmc.2022.21830.1113ENMehranGabraniDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, Iran0000-0002-4489-0477BahmanRezaeiFaculty of Science, Urmia University, Urmia, IranEsraSengelen SevimDepartment of Mathematics, Istanbul Bilgi University, 34060, Eski Silahtaraga Elektrik Santrali
Kazim Karabekir Cad. No: 2/13 Eyupsultan, Istanbul, TurkeyJournal Article20221007The Ricci curvature is introduced by spray on M<sup>n</sup>. Sprays are deformed to projective sprays with a volume form dV on M<sup>n</sup>. 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.https://ajmc.aut.ac.ir/article_4984_726e78219886e354785dbcc7d156f6fb.pdf