论文标题
在投影的RICCI曲率上
On the projective Ricci curvature
论文作者
论文摘要
RICCI曲率的概念定义为在歧管上喷洒的概念。用歧管上的体积形式形式，每个喷雾都可以变形为投影喷雾。投影喷雾的RICCI曲率称为投射RICCI曲率。在本文中，我们介绍了Ricci-Flat Sprays的概念。我们为具有非负RICCI曲率的Ricci-Flat喷雾剂建立了全球刚度结果。然后，我们研究和描述Ricci-Flat Randers指标。
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.
