A Duality Between Compact Symmetric Triads and Semisimple Pseudo-Riemannian Symmetric Pairs with Applications to Geometry of Hermann Type Actions
A Duality Between Compact Symmetric Triads and Semisimple Pseudo-Riemannian Symmetric Pairs with Applications to Geometry of Hermann Type Actions
复制标题
紧对称三元组与半简单伪黎曼对称对之间的对偶及其在赫尔曼型作用几何中的应用
DOI：
10.1007/978-981-10-5556-0_18
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Sasaki Atsumu
中科院分区：
文献类型：
--
作者：
Baba Kurando;Ikawa Osamu;Sasaki Atsumu
本文为参考文献[1-3]中未发表论文的综述论文。引入交换紧对称三元组与半单伪黎曼对称对之间的对偶性概念，这是紧/非紧黎曼对称对之间对偶性的推广。作为其应用，我们从紧对称三角的角度给出了Berger的半简单伪黎曼对称对分类的另一种证明。更确切地说，我们利用第二作者介绍的对称三元组理论，给出了交换紧对称三元组与半简单伪黎曼对称三元组之间的一一对应关系的显式描述。我们还研究了伪黎曼对称空间eg /H上的对称子群的作用，称为Hermann型作用。详见[1-3]。
This is a survey paper of not-yet-published papers listed in the reference as [1–3]. We introduce the notion of a duality between commutative compact symmetric triads and semisimple pseudo-Riemannian symmetric pairs, which is a generalization of the duality between compact/noncompact Riemannian symmetric pairs. As its application, we give an alternative proof for Berger’s classification of semisimple pseudo-Riemannian symmetric pairs from the viewpoint of compact symmetric triads. More precisely, we give an explicit description of a one-to-one correspondence between commutative compact symmetric triads and semisimple pseudo-Riemannian symmetric pairs by using the theory of symmetric triads introduced by the second author. We also study the action of a symmetric subgroup ofGon a pseudo-Riemannian symmetric spaceG/H, which is called a Hermann type action. For more details, see [1–3].