Totally geodesic submanifolds in Riemannian symmetric spaces

TL;DR

This paper reviews key constructions and classifications of totally geodesic submanifolds in Riemannian symmetric spaces, and presents new classification results specifically for rank 2 spaces.

Contribution

It provides a comprehensive summary of existing classification results and introduces new classifications for totally geodesic submanifolds in rank 2 symmetric spaces.

Findings

Summarized major constructions and classifications in the field.

Presented new classification results for rank 2 symmetric spaces.

Enhanced understanding of the structure of totally geodesic submanifolds.

Abstract

In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification of the totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2.