Invariant Einstein metrics on three-locally-symmetric spaces

TL;DR

This paper classifies three-locally-symmetric spaces for compact simple Lie groups and identifies all invariant Einstein metrics on these spaces, advancing understanding of their geometric structures.

Contribution

It provides a complete classification of three-locally-symmetric spaces and determines all invariant Einstein metrics on them, a novel comprehensive analysis.

Findings

Classification of three-locally-symmetric spaces for compact simple Lie groups

Complete list of invariant Einstein metrics on these spaces

New insights into the geometric structures of these spaces

Abstract

In this paper, we classify three-locally-symmetric spaces for a connected, compact and simple Lie group. Furthermore, we give the classification of invariant Einstein metrics on these spaces.