标题： 外齐性子流形的典范约化分解 显示英文标题

标题： Canonical Reductive Decomposition of Extrinsic Homogeneous Submanifolds

摘要： 设$\overline{M}=\overline{G}/\overline{H}$为一个齐次黎曼流形。 给定一个李子群$G\subset \overline{G}$和$\overline{M}$的齐次结构的一个约化分解，我们分析作用下$G$轨道的典范约化分解。 这些$G$-作用的叶是外齐次子流形，并且它们的约化分解的分析与其外在性质有关。 我们将研究与文献中的工作联系起来，并开始与阿姆布罗斯-辛格定理和子流形的齐次结构建立关系。 显示英文摘要

摘要： Let $\overline{M}=\overline{G}/\overline{H}$ be a homogeneous Riemannian manifold. Given a Lie subgroup $G\subset \overline{G}$ and a reductive decomposition of the homogeneous structure of $\overline{M}$, we analyze a canonical reductive decomposition for the orbits of the action of $G$. These leaves of the $G$-action are extrinsic homogeneous submanifolds and the analysis of the reductive decomposition of them is related with their extrinsic properties. We connect the study with works in the literature and initiate the relationship with the Ambrose-Singer theorem and homogeneous structures of submanifolds.