双曲空间形式中具有常平均曲率的超曲面(英文)  

HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

作　　者：韩英波[1] 冯书香[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《数学杂志》2014年第4期633-639,共7页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10971029;11201400;11026062);Project of Henan Provincial Department of Education(2011A110015);Talent Youth Teacher Fund of Xinyang Normal University

摘　　要：本文研究了双曲空间形式H^(n+1)(—1)中具有常平均曲率及两个离散主曲率(其中一个主曲率是1-重)的完备连通可定向的n-维超曲面M^n.利用活动标架,得到如果M^n的基本形式的模长满足刚性条件(1.3),那么M^n同构双曲柱面.In the paper, we study an ndimensional complete connected and oriented hypersurface MN in H^n＋1（-1） with constant mean curvature and two distinct principal curvatures, one of which is simple. By using the moving frames, we obtain that if the squared norm of second fundamental form of M^n satisfies a rigidity condition （1.3）, the M^n is isometric to hyperbolic cylinder.

关 键 词：超曲面 双曲空间形式 常平均曲率 

分 类 号：O186.1[理学—数学]