On the projective Ricci curvature
Differential Geometry
2020-08-05 v1
Abstract
The notion of the Ricci curvature is defined for sprays on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. In this paper, we introduce the notion of projectively Ricci-flat sprays. We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature. Then we study and characterize projectively Ricci-flat Randers metrics.
Keywords
Cite
@article{arxiv.2008.01350,
title = {On the projective Ricci curvature},
author = {Zhongmin Shen and Liling Sun},
journal= {arXiv preprint arXiv:2008.01350},
year = {2020}
}