| 单位球面中具有平行平均曲率向量的子流形(英文) |
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| 引用本文： | 侯晓阳.单位球面中具有平行平均曲率向量的子流形(英文)[J].淮北煤炭师范学院学报(自然科学版),2009,30(1). |
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| 作者姓名： | 侯晓阳 |
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| 作者单位： | 温州大学城市学院,浙江,温州,325035 |
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| 摘 要： | 设Mn是单位球面Sn+P中具有平行平均曲率向量的紧致可定向子流形,令|A|2为第二本形式长度的平方.若|A|2< 2n(√)n-1/2θ(√)n-1+n,则Mn是Sn+P中的标准球面;当|A|2< 2n(√)n-1/2θ(√)n-1+n时,还可以对子流形Mn进行分类.
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| 关 键 词： | 平行平均曲率 第二基本形式 紧致 全脐 |
Submanifolds in a Unit Sphere with Parallel Mean Curvature Vector |
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| HOU Xiaoyang.Submanifolds in a Unit Sphere with Parallel Mean Curvature Vector[J].Journal of Huaibei Coal Industry Teachers College(Natural Science edition),2009,30(1). |
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| Authors: | HOU Xiaoyang |
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| Institution: | HOU Xiao- yang (City College of Wenzhou University,325035,Wenzhou,Zhejiang,China) |
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| Abstract: | Let Mn be a compact submanifold with parallel mean curvature vector immersed in the unit sphere Sn+P, Denote by |A|2 the square of the length of its second fundamental form. If then │A│2=2n(√)n-1/2θ(√)n-1+n,Mn is a stan-dard sphere in Sn+P. We can also characterize Mn with │A│2=2n(√)n-1/2θ(√)n-1+n. |
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| Keywords: | parallel mean curvature second fundamental form compact totally umbilical |
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