一类流形的刚性定理(英文)  

A Rigidity Theorem for Manifold with a Nice Submanifold

作　　者：徐森林[1] 黄正[1] 祁锋[1] 

机构地区：[1]中国科技大学数学系

出　　处：《应用数学》1999年第1期72-75,共4页Mathematica Applicata

摘　　要：本文通过具有良好性质的子流形的存在性，证明了一类流形的一个刚性定理，并得到形如Ｂｏｎｎｅｔ－Ｍｙｅｒｓ定理的推论．我们还指出，在主要定理中全测地子流形的条件一般不能减弱为极小子流形．In this paper,we prove a rigidity theorem for a complete Riemannian manifold by the existence of a nice totally geodesic submanifold.Then we state a corollary which has the form of the well known Bonnet Myers theorem.We also point out that in our main theorem,'totally geodesic' can not be taken place by 'minimal' in our way.

关 键 词：RICCI曲率 全测地子流形 刚性定理 流形 

分 类 号：O19[理学—数学]