共形平坦的黎曼流形  

Conformally Flat Riemannian Manifolds

作　　者：李潇寰[1] 郭瑞芝[2] 

机构地区：[1]株洲职业技术学院,湖南株洲412001 [2]湖南师范大学数学系,长沙410081

出　　处：《湖南理工学院学报（自然科学版）》2009年第3期19-22,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

摘　　要：研究了共形平坦的黎曼流形(Mn,g)(n≥4),建立了一个关于紧致流形的Simons型的积分不等式.如果(Mn,g)是共形平坦的,且它的Ricci曲率满足一定的条件,利用该积分不等式给出(Mn,g)的在等距群下的分类.In this paper,conformally flat Riemannian manifolds （ M^n,g ）is investigated and a Simons integral inequality is established. If （ M^n,g ） is compact. If （ M^n,g ） is conformally flat and Ricci curvature satisfy some conditions,the classification of the isometric group of （ M^n,g ）is obtained by using the integral inequality.

关 键 词：共形平坦的黎曼流形 RICCI曲率 Weyl张量 

分 类 号：O186.12[理学—数学]