| 黎曼流形中紧子流形的拼挤定理 |
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| 引用本文： | 程立正. 黎曼流形中紧子流形的拼挤定理[J]. 数学理论与应用, 2008, 28(3): 73-76 |
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| 作者姓名： | 程立正 |
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| 作者单位： | 湖南涉外经济学院理学部,长沙 410205 |
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| 摘 要： | 本利用几何不等式和曲率估计的方法，证明了黎曼流形N^n＋p,上的具有平行平均曲率的紧子流形M^n上的一个拼挤定理。若N上的截曲率KN满足- 1≤ KN≤δ≤0，且‖S- nH2‖n/2, ‖ S-nH^2‖n/n-s满足一些不等式，则δ= - 1。
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| 关 键 词： | 拼挤定理 子流形 非负截曲率 |
Pinching Theorem for Compact Submanifold in Riemannian Manifold |
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| Cheng Lizheng. Pinching Theorem for Compact Submanifold in Riemannian Manifold[J]. Mathematical Theory and Applications, 2008, 28(3): 73-76 |
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| Authors: | Cheng Lizheng |
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| Affiliation: | Cheng Lizheng (Depamnent of Mathematics, Hunan International Economics University, Chansha, 410205 ) |
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| Abstract: | Making use of geometric inequalities and curvature estimates, I prove a pinching theorem of compact submanifolds M^n with parallel mean curvature in a complete simply conneted Riemannian manifold N^n＋p with nonpositive sectional curva- ture.If the sectional curvature of N KN satisfy - 1≤ KN≤δ≤0. and ‖S- nH2‖n/2, ‖ S-nH^2‖n/n-s satisfy some inequalities,then δ= - 1. |
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| Keywords: | Pinching theorem Submanifold Nonpositive sectional curvature |
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