| 球面中具有平行平均曲率向量的子流形 |
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| 引用本文： | 成庆明,孙华飞.球面中具有平行平均曲率向量的子流形[J].东北大学学报(自然科学版),1992(2). |
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| 作者姓名： | 成庆明 孙华飞 |
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| 作者单位： | 东北工学院数学系
(成庆明)，东北工学院数学系(孙华飞) |
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| 摘 要： | 研究了单位球面中具有平行平均曲率向量的子流形的第二基本形式模长平方的Pinching 问题,得到了优于Yau 和莫小欢的 Pinching 常数,并获得更强的几何结论,即子流形是全脐的。另外,还把文献2]的结论推广到了子流形是完备的情形。
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| 关 键 词： | 平行平均曲率向量 全脐子流形 全测地子流形 |
Submanifolds in Unit Sphere with Parallel Mean Curvature Vector |
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| Cheng Qingming,Sun Huafei.Submanifolds in Unit Sphere with Parallel Mean Curvature Vector[J].Journal of Northeastern University(Natural Science),1992(2). |
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| Authors: | Cheng Qingming Sun Huafei |
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| Institution: | Cheng Qingming;Sun Huafei |
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| Abstract: | Studies the pinching problem of the square of length of second fundamentalform of submanifolds in a unit sphere with parallel mean curvature vector. Apinching constant which is sharper than that of Yau and Mo is obtained and astronger geometric conclusion is reached,i. e. the submanifold is tot ally umbili-cal. Also,the conclusion in2]is generalized to such cases that the submanifoldis complete. |
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| Keywords: | parallel mean curvature vector totally umbilical submanifold totally geodesic submanifold |
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