数学杂志2017，Vol.37Issue(4)：672-684,13.
黎曼流形在正交联络下的全脐点子流形
TOTALLY UMBILICAL SUBMANIFOLD ON RIEMANNIAN MANIFOLD WITH AN ORTHOGONAL CONNECTION
摘要
Abstract
In this paper, we investigate the fundamental equations of submanifolds under or-thogonal 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 to-tally umbilical submanifolds on spaces with constant curvature, which generalizes the results under the Levi-Civita connection.关键词
正交联络/黎曼流形的基本方程/子流形/脐点Key words
orthogonal connections/fundamental equations in Riemannian manifolds/sub-manifold/umbilical point分类
数理科学引用本文复制引用
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):672-684,13.基金项目
Supported by National Natural Science Foundation of China (11571259). （11571259）
