| 常曲率流形中具平行李奇曲率的超曲面 |
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| 引用本文： | 李同柱,郭震. 常曲率流形中具平行李奇曲率的超曲面[J]. 数学学报, 2004, 47(3): 587-592. DOI: cnki:ISSN:0583-1431.0.2004-03-021 |
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| 作者姓名： | 李同柱 郭震 |
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| 作者单位： | 云南师范大学数学学院,昆明,650092 |
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| 基金项目： | 国家自然科学基金(10261010)，云南省自然科学基金(2002A00031M) |
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| 摘 要： | 设f:M~n→M~(n+1)(c)为具平行李奇曲率的黎曼流形到常曲率流形的等距浸入,本文给出了该超曲面的分类。另外,若M~n还是极小超曲面,本文也给出了该超曲面的分类,推广了Lawson的有关结果。
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| 关 键 词： | 平行李奇曲率 不可约流形 Gauss方程 |
| 文章编号： | 0583-1431(2004)03-0587-06 |
Hypersurfaces with Parallel Ricci Curvature in Constantly Curved Manifold |
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| Tong Zhu LI,Zhen GUO. Hypersurfaces with Parallel Ricci Curvature in Constantly Curved Manifold[J]. Acta Mathematica Sinica, 2004, 47(3): 587-592. DOI: cnki:ISSN:0583-1431.0.2004-03-021 |
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| Authors: | Tong Zhu LI Zhen GUO |
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| Affiliation: | Tong Zhu LI;Zhen GUO Department of Mathematics, Yunnan Normal University, Kunming 650092, P. R. China |
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| Abstract: | Let f: M~n→ (c) be an isometric immersion of a Riemannian manifoldwith parallel Ricci curvature into a constantly curved manifold. In this paper, wepresent the classification of this kind of hypersurfaces. In addition, if (M~n, f) is aminimal immersion, we also classify this class of hypersurfaces and extend the resultsof Lawson. |
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| Keywords: | Parallel Ricci curvature Irreducible manifold Gauss equation |
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