具有调和曲率张量的拟爱因斯坦流形

On the Quasi-Einsteinian Manifold with Harmonic Curvature Tensor

本文讨论了拟爱因斯坦流形定义中的两个数量函数及生成元与调和曲率张量的关系,给出了具有调和曲率张量的拟爱因斯坦流形的一个充要条件,即数量函数及生成元应满足的微分方程。同时,做为特例,也考虑了拟常曲率流形中的类似问题。

Discusses the relationships among the two numerical functions involved in the definition of quasi-Einsteinian manifold, the generating element and the harmonic curvature tensor. A necessary and sufficient condition is thus given for an Einsteinian manifold with harmonic curvature tensor, i.e., a differential equation that both the numerical functions and the generating element should satisfy. As a particular case, the similar problem in quasi-constant curvature manifold is also taken into consideration.