| 局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形 |
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| 引用本文： | 段仁杰,陈抚良,何水军.局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形[J].江西科学,2011,29(3):307-309,312. |
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| 作者姓名： | 段仁杰 陈抚良 何水军 |
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| 作者单位： | 江西师范大学数学与信息科学学院,江西南昌,330022 |
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| 摘 要： | 设Mn为Sn+p中的紧致子流形,∪M=∪x∈M∪Mx是M的单位切丛,文献1]通过引入函数f(x)=maxu,v∈Mx‖B(u,u)-B(v,v)‖2,其中B是M的第2基本形式,进行研究得到一个pinching定理。将球面空间中的类似问题推广到局部对称共形平坦空间中得到一个主要定理。
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| 关 键 词： | 局部对称 共形平坦 Ricci曲率 |
On Compact Submanifolds in a Locally Symmetric and Conformally Flat Riemannian Maniflod with Parallel Mean Curvature |
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| DUAN Ren-jie,CHEN Fu-liang,HE Shui-jun.On Compact Submanifolds in a Locally Symmetric and Conformally Flat Riemannian Maniflod with Parallel Mean Curvature[J].Jiangxi Science,2011,29(3):307-309,312. |
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| Authors: | DUAN Ren-jie CHEN Fu-liang HE Shui-jun |
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| Institution: | (College of Mathematics and Information Science,Jiangxi Normal University,Jiangxi Nanchang 330022 PRC) |
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| Abstract: | Let Mn be a compact submanifolds of unit sphere Sn＋p,∪M=∪x∈M ∪Mx is the unit tangent bundle on M.The paper1] constructed a function f（x）=maxu,v∈Mx‖B（u,u）-B（v,v）‖2,where B is the second fundamental form of M,which obtained a Pinching theorem.In this paper,the similar problems in space of unit sphere are popularized in the space of locally symmetry and conformally flat space. |
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| Keywords: | Locally symmetric Conformally flat Ricci curvature |
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