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.
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In Memory of Professor Zhengguo Bai (1916–2015)
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Shen, Z., Sun, L. On the projective Ricci curvature. Sci. China Math. 64, 1629–1636 (2021). https://doi.org/10.1007/s11425-020-1705-x
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DOI: https://doi.org/10.1007/s11425-020-1705-x