On the projective Ricci curvature In Memory of Professor Zhengguo Bai(1916-2015)

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.

Automated summary

This paper introduces the concept of projectively Ricci-flat sprays and establishes global rigidity result for them with nonnegative Ricci curvature. Further study and characterization of projectively Ricci-flat Randers metrics are also conducted.