| 常曲率空间中的伪脐点子流形 |
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| 引用本文： | 陈咸平.常曲率空间中的伪脐点子流形[J].华东师范大学学报(自然科学版),1989(1):59-65. |
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| 作者姓名： | 陈咸平 |
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| 作者单位： | 华东师范大学数学系 |
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| 摘 要： | 本文研究常曲率Riemann流形中具有平行平均曲率的伪脐点子流形。得到了一个Simons型公式和一个相应的Pinching定理,并确定了球面中所有0≤S-nH~2≤n(H~2+C)/(2-1/P-1)的这类子流形或者是全脐点的,或者是Clifford环面,或者是Veroness曲面。
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| 关 键 词： | 平行均曲率 伪脐点子流形 |
Pseudo-umbilical Submanifolds in Spaces of Constant Curvature |
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| CHEN XIANPING.Pseudo-umbilical Submanifolds in Spaces of Constant Curvature[J].Journal of East China Normal University(Natural Science),1989(1):59-65. |
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| Authors: | CHEN XIANPING |
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| Institution: | Department of Mathematics |
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| Abstract: | The pseudo-umbilical n-submanifolds with parallel mean ourvature in(n+p)-Riemannian manifold of constant curvature c are considered. A formula of Simons'type and therefore a Pinching theorem are obtained. It is proved that such submanifolds in a sphere with are totally umbilical submanifolds, Clifford minimal hypersurfaces in a hypersphere, or Veroness surfaces in 4-sphere. |
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| Keywords: | parallel mean curvature pseudo-umbilical submanifold totally umbilical submanifold |
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