| 关于单位球面中偶维数子流形的一个球定理 |
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| 引用本文： | 胡泽军,翟书杰.关于单位球面中偶维数子流形的一个球定理[J].郑州大学学报(理学版),2005,37(1):1-4. |
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| 作者姓名： | 胡泽军 翟书杰 |
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| 作者单位： | 郑州大学数学系,郑州,450052 |
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| 基金项目： | 河南省杰出青年科学基金，教育部留学回国人员科研启动基金 |
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| 摘 要： | 从子流形几何的观点出发,得到了关于单位球面中偶维数子流形Mn的一个拓扑球定理.例子表明该结果是最佳的.这个球定理与Th.Vlachos最近的一个结果相对,他得到了球面中奇维数子流形的一个球定理,其关于维数的假定是本质的.
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| 关 键 词： | 李奇曲率 平均曲率向量 同胚 同调群 |
A Sphere Theorem for Even-dimensional Submanifolds of the Unit Sphere |
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| Hu Zejun,Zhai Shujie.A Sphere Theorem for Even-dimensional Submanifolds of the Unit Sphere[J].Journal of Zhengzhou University:Natural Science Edition,2005,37(1):1-4. |
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| Authors: | Hu Zejun Zhai Shujie |
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| Abstract: | A topological sphere theorem from the point of view of submanifold geometry for even-dimensional submanifolds M n in the unit sphere is established.There are some examples which show that the result is optimal.This sphere theorem is the counterpart of the very recent result of Th.Vlachos who obtained such a sphere theorem for odd-dimensional submanifolds and his assumption on the dimension is essential. |
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| Keywords: | Ricci curvature mean curvature vector homeomorphic homology group |
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