On the projective Ricci curvature

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...

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Bibliographic Details
Published inScience China. Mathematics Vol. 64; no. 7; pp. 1629 - 1636
Main Authors Shen, Zhongmin, Sun, Liling
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.07.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Curvature
Manifolds
Mathematics
Mathematics and Statistics
53B40
spray
Finsler metric
53C60
Randers metric
projective Ricci curvature
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-020-1705-x