Weighted Projective Ricci Curvature in Finsler Geometry
Differential Geometry
2019-08-27 v1
Abstract
In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.
Keywords
Cite
@article{arxiv.1908.09465,
title = {Weighted Projective Ricci Curvature in Finsler Geometry},
author = {T. Tabatabaeifar and B. Najafi and A. Tayebi},
journal= {arXiv preprint arXiv:1908.09465},
year = {2019}
}