球空间具平行单位平均曲率向量的完备子流形  

Submanifolds with parallel normalized mean curvature vector in a sphere

作　　者：王美娇[1] 

机构地区：[1]广州大学理学院,广东广州510405

出　　处：《广州大学学报（自然科学版）》2004年第4期299-302,共4页Journal of Guangzhou University:Natural Science Edition

摘　　要：设M是n维完备黎曼流形,等距浸入(n+p)维单位球空间Sn+p,具有平行的单位平均曲率向量.则或者M局部地是Sn+p的一个(n+1)维全测地子流形Sn+1中的超曲面片;或者supSa≥n.其中supS是M的第二基本形式长度的平方的上确界.进一步,若n≤7,或者M整体地是Sn+p的一个(n+1)维全测地子流形Sn+1中的超曲面;或者supS(1+12sgn(p-2))>n.所得结果推广了具有平行的平均曲率向量的紧致子流形的结果.The complete submanifolds with parallel unit mean curvature vector in a sphere S^(n+p)(p>1) are studied, with some characteristics of these submanifolds obtained by using the generalized maximal principle. It is shown that if M is complete submanifolds with parallel mean curvature vector in S^(n+p), then S=Sn+1, M is a hypersurface of a n+1 dimensional totally geodesic submanifolds S^(n+1) of S^(n+p), or sup Sa≥n. And it is further shown that if n≤7, then S=S(n+1), M is a hypersurface of a n+1 dimensional totally geodesic submanifolds S^(n+1) of S^(n+p), or sup S(1+12 sgn (p-2))>n.

关 键 词：平均曲率向量 第二基本形式 完备子流形 

分 类 号：O186.12[理学—数学]