| 双曲空间形式中具有常平均曲率的超曲面(英文) |
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| 引用本文： | 韩英波,冯书香.双曲空间形式中具有常平均曲率的超曲面(英文)[J].数学杂志,2014,34(4):633-639. |
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| 作者姓名： | 韩英波 冯书香 |
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| 作者单位： | 信阳师范学院数学与信息科学学院, 河南 信阳 464000,信阳师范学院数学与信息科学学院, 河南 信阳 464000 |
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| 基金项目： | 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. |
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| 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.
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| 关 键 词： | 超曲面 双曲空间形式 常平均曲率 |
| 收稿时间： | 2012/3/5 0:00:00 |
| 修稿时间： | 2012/11/5 0:00:00 |
HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE |
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| HAN Ying-bo and FENG Shu-xiang.HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE[J].Journal of Mathematics,2014,34(4):633-639. |
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| Authors: | HAN Ying-bo and FENG Shu-xiang |
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| Institution: | College of Math. and Information Science, Xinyang Normal University, Xinyang 464000, China and College of Math. and Information Science, Xinyang Normal University, Xinyang 464000, China |
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| Abstract: | In the paper,we study an n-dimensional complete connected and oriented hypersurface MN in Hn+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 Mn satisfies a rigidity condition (1.3),the Mn is isometric to hyperbolic cylinder. |
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| Keywords: | hypersurfaces hyperbolic space form constant mean curvature |
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