关于拟Einstein流形  

On Quasi-Einsteinian Manifolds

作　　者：李中林[1] 

机构地区：[1]杭州大学数学系

出　　处：《杭州大学学报（自然科学版）》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

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.

关 键 词：黎曼流形 EINSTEIN流形 Ricci循环 

分 类 号：O186.12[理学—数学]