摘要
本文首先讨论了拟Einstein流形QE的一些基本性质,求得了QE流形的几何和代数特征。其次,探求了一个Riemann流形为QE流形的条件。最后,讨论了QE流形与一些熟知Riemann流形之间的关系,指出了某些QE流形的不存在性。
In this paper, we have found the geometric and algebraic characteristics of QE(ξ) manifold, and we have established the following main theorems: Theorem 1. In a Riemannian manifold, the relations
and
and
are mutually equivalent.
Theorem 2. A QE(ξ) manifold is Rieci-symmetric, iff the manifold is Einstein, or its basic element ξ is a parallel vector field.
Theorem 3. The Ricci-recurrent, the Riemannian-recurrent and the essentially conformally symmetric or essentially 2-recurrent QE manifold are not existent.
出处
《杭州大学学报（自然科学版）》
CSCD
1989年第2期115-122,共8页
Journal of Hangzhou University Natural Science Edition
基金
国家自然科学基金资助项目
关键词
黎曼流形
EINSTEIN流形
Ricci循环
Riemannian manifold
quasi-Einsteinian manifold
Ricci principal direction
Ricci-symmetric
Ricci-recurrent
essentially conformally symmetric
essentially 2-recurrent
