Classification of invariant AHS--structures on semisimple locally symmetric spaces

TL;DR

This paper classifies semisimple locally symmetric spaces that admit invariant AHS-structures, detailing their types and equivalence classes, thereby advancing understanding of geometric structures compatible with symmetry.

Contribution

It provides a comprehensive classification of invariant AHS-structures on semisimple locally symmetric spaces, including their equivalence classes, which was previously unexplored.

Findings

Identified all semisimple locally symmetric spaces admitting invariant AHS-structures.

Determined the classification and equivalence classes of these structures.

Extended the understanding of geometric structures compatible with local symmetries.

Abstract

In this article, we discuss which semisimple locally symmetric spaces admit an AHS--structure invariant to local symmetries. We classify them for all types of AHS--structures and determine possible equivalence classes of such AHS--structures.