| 一类流形的刚性定理 |
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| 引用本文： | 徐森林,黄正.一类流形的刚性定理[J].应用数学,1999,12(1):72-75. |
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| 作者姓名： | 徐森林 黄正 |
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| 作者单位： | 中国科技大学数学系 |
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| 摘 要： | 本文通过具有良好性质的子流形的存在性，证明了一类流形的一个刚性定理，并得到形如Ｂｏｎｎｅｔ－Ｍｙｅｒｓ定理的推论．我们还指出，在主要定理中全测地子流形的条件一般不能减弱为极小子流形．
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| 关 键 词： | 第k个Ricci曲率 全测地子流形 刚性定理 |
A Rigidity Theorem for Manifold with a Nice Submanifold |
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| Xu Senlin Huang Zheng Qi,Feng.A Rigidity Theorem for Manifold with a Nice Submanifold[J].Mathematica Applicata,1999,12(1):72-75. |
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| Authors: | Xu Senlin Huang Zheng Qi Feng |
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| Abstract: | In
this paper,we prove a rigidity theorem for a complete Riemannian manifold by the existence of a
nice totally geodesic submanifold.Then we state a corollary which has the form of the well known
Bonnet Myers theorem.We also point out that in our main theorem,"totally geodesic" can not be
taken place by "minimal" in our way. |
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| Keywords: | K th Ricci curvature Totally geodesic submanifold Rigidity theorem |
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