Totally geodesic submanifolds in products of rank one symmetric spaces

TL;DR

This paper classifies totally geodesic submanifolds in products of rank one symmetric spaces and provides examples of irreducible submanifolds with non-trivial Kähler angles in Hermitian symmetric spaces.

Contribution

It offers a comprehensive classification of totally geodesic submanifolds in these spaces and introduces new examples with unique geometric properties.

Findings

Classification of submanifolds in product spaces

Existence of irreducible submanifolds with non-trivial Kähler angles

Infinitely many examples in Hermitian symmetric spaces

Abstract

In this article we classify totally geodesic submanifolds in arbitrary products of rank one symmetric spaces. Furthermore, we give infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces with non-trivial constant K\"ahler angle, i.e. they are neither complex nor totally real.