# Submanifold geometry in symmetric spaces of noncompact type

## TL;DR

This survey introduces submanifold geometry in symmetric spaces of noncompact type, focusing on examples, classification problems, and special submanifold types such as isoparametric and homogeneous CPC submanifolds.

## Contribution

It provides an overview of the construction and classification of various submanifolds and actions in noncompact symmetric spaces, highlighting recent developments.

## Key findings

- Classification of homogeneous and isoparametric hypersurfaces
- Construction methods for submanifolds in noncompact symmetric spaces
- Analysis of polar and hyperpolar actions

## Abstract

In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar and hyperpolar actions, and homogeneous CPC submanifolds.