| Lorentz-Minkowski空间中的乘积空间R~k×H~(n-k) |
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| 引用本文： | 张远征.Lorentz-Minkowski空间中的乘积空间R~k×H~(n-k)[J].数学学报,2007,50(2):325-332. |
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| 作者姓名： | 张远征 |
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| 作者单位： | 上海财经大学应用数学系,上海200433 |
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| 摘 要： | 本文的主要结果是:Lorentz-Minkowski空间中介于两个同心伪圆柱面之间的完备、类空、常平均曲率超曲面必为伪圆柱面,即乘积空间R~k×H~(n-k)．对于常高阶平均曲率的情况,如果截曲率有下界,那么介于两个同心伪球面之间的完备类空超曲面必为伪球面．
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| 关 键 词： | 类空超曲面 平均曲率 广义极大原理 |
| 文章编号： | 0583-1431（2007）02-0325-08 |
| 收稿时间： | 2005-9-29 |
| 修稿时间： | 2005-09-28 |
On the Product Space R~k×H~(n-k) in Lorentz-Minkowski Space |
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| Yuan Zheng ZHANG.On the Product Space R~k×H~(n-k) in Lorentz-Minkowski Space[J].Acta Mathematica Sinica,2007,50(2):325-332. |
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| Authors: | Yuan Zheng ZHANG |
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| Institution: | Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China |
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| Abstract: | In this paper,we show that the only complete spacelike hypersurfaces with constant mean curvature in Lorentz-Minkowski space which are bounded be- tween two concentric hyperbolic cylinders are the hyperbolic cylinders,i.e.,the product R~k×H~(n-k).In the case of constant higher mean curvature,if the sectional curvature is bounded from below,then the only complete spacelike hypersurfaces in Lorentz- Minkowski space which are bounded between two concentric hyperbolic spaces are the hyperbolic spaces. |
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| Keywords: | spacelike hypersurfaces mean curvature generalized maximal principle |
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