On the realization of Riemannian symmetric spaces in Lie groups

TL;DR

This paper presents a method to realize certain Riemannian symmetric spaces as closed submanifolds within Lie groups, providing multiple equivalent representations and analyzing related coset structures.

Contribution

It introduces a novel realization of symmetric spaces as submanifolds in Lie groups and explores their properties and representations.

Findings

Realization of symmetric spaces as closed submanifolds in Lie groups

Multiple equivalent representations of the submanifold P

Analysis of intersections with coset spaces gK

Abstract

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK\cap P are also discussed, where gK is a coset space in G.