局部对称空间中线性Weingarten超曲面  

Linear Weingarten Hypersurfaces in Locally Symmetric Manifolds

作　　者：张亚娟[1] 刘建成[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《华南师范大学学报（自然科学版）》2016年第6期124-128,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11261051)

摘　　要：研究了局部对称空间中具有有界平均曲率的可定向完备线性Weingarten超曲面的刚性分类.在对超曲面的全脐张量Φ的模长进行适当限制下,应用广义极大值原理,得到了该类超曲面是全脐的或等距于一个具有2个不同主曲率的超曲面,且其中一个主曲率的重数为1.The rigidity classifications for complete orientable linear Weingarten hypersurfaces with bounded mean curvature in locally symmetric manifold are studied. By supposing a suitable restriction on the norm of the totally umbilical tensor Φ and using the generalized maximum principle,it is proved that such a hypersurface must be either totally umbilical or isometric to the hypersurface with two distinct principal curvatures,one of which is simple.

关 键 词：线性Weingarten超曲面 局部对称 δ-拼挤 平均曲率 

分 类 号：O186.12[理学—数学]