Shen, ZhongminSun, Liling2022-01-112022-01-112020-07Shen, Z., & Sun, L. (2020). On the projective Ricci curvature. Science China Mathematics. https://doi.org/10.1007/s11425-020-1705-x1869-1862https://hdl.handle.net/1805/27352The 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.enPublisher PolicyRicci curvatureprojective sprayprojectively Ricci-flat spraysArticle