# Real structures on symmetric spaces

## TL;DR

This paper establishes a criterion for the existence of equivariant real structures on complex symmetric spaces associated with semisimple groups and explains how to classify their equivalence classes.

## Contribution

It provides a necessary and sufficient condition for real structures and a method to determine their number of equivalence classes.

## Key findings

- Derived a criterion for real structures on symmetric spaces.
- Provided a classification method for equivalence classes.
- Enhanced understanding of symmetry in complex geometric structures.

## Abstract

We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces for semisimple groups and discuss how to determine the number of equivalence classes for such structures.