On the projective Ricci curvature

被引：0
|
作者：
Shen Z. [1 ]
Sun L. [2 ,3 ]
机构：
[1] Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, 46202, IN
[2] Department of Mathematics, Taiyuan University of Technology, Taiyuan
[3] School of Science, Jimei University, Xiamen
来源：
Science China Mathematics | 2021年 / 64卷 / 7期
关键词：
53B40; 53C60; Finsler metric; projective Ricci curvature; Randers metric; spray;
D O I：
10.1007/s11425-020-1705-x
中图分类号：
学科分类号：
摘要：
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. © 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.
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页码：1629 / 1636
页数：7
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