| 黎曼流形在正交联络下的全脐点子流形 |
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| 引用本文： | 李凯鹏,王旭升.黎曼流形在正交联络下的全脐点子流形[J].数学杂志,2017,37(4):672-684. |
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| 作者姓名： | 李凯鹏 王旭升 |
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| 作者单位： | 武汉大学数学与统计学院, 湖北 武汉 430072,武汉大学数学与统计学院, 湖北 武汉 430072 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11571259). |
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| 摘 要： | 本文研究了正交联络下子流形基本方程以及在全脐点子流形中的应用.利用Cartan的方法将挠率张量分解成三个部分，计算得到正交联络下的三个基本方程，并考虑一个特殊的正交联络，证明了其黎曼曲率会有类似于Levi-Civita联络下的性质.利用基本方程得到常曲率空间中的全脐点子流形的性质，推广了Levi-Civita联络下的相应结果.
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| 关 键 词： | 正交联络 黎曼流形的基本方程 子流形 脐点 |
| 收稿时间： | 2017/1/10 0:00:00 |
| 修稿时间： | 2017/3/27 0:00:00 |
TOTALLY UMBILICAL SUBMANIFOLD ON RIEMANNIAN MANIFOLD WITH AN ORTHOGONAL CONNECTION |
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| LI Kai-peng and WANG Xu-sheng.TOTALLY UMBILICAL SUBMANIFOLD ON RIEMANNIAN MANIFOLD WITH AN ORTHOGONAL CONNECTION[J].Journal of Mathematics,2017,37(4):672-684. |
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| Authors: | LI Kai-peng and WANG Xu-sheng |
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| Institution: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China and School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | In this paper, we investigate the fundamental equations of submanifolds under orthogonal connections and apply the results in totally umbilical submanifolds. By using the method of Cartan to split the torsion tensor into three components, we calculate and attain the fundamental equations. We consider a special orthogonal connection with which the Riemannian curvature has the same properties as the Levi-Civita connection. We use the fundamental equations to argue totally umbilical submanifolds on spaces with constant curvature, which generalizes the results under the Levi-Civita connection. |
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| Keywords: | orthogonal connections fundamental equations in Riemannian manifolds submanifold umbilical point |
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