Hyperpolar actions on reducible symmetric spaces

TL;DR

This paper classifies hyperpolar actions on reducible symmetric spaces of the compact type, showing they are either orbit equivalent to Hermann actions or of cohomogeneity one, thus providing a comprehensive understanding of such symmetries.

Contribution

It proves that indecomposable hyperpolar actions on these spaces are either Hermann actions or of cohomogeneity one, offering a complete classification.

Findings

Indecomposable hyperpolar actions are orbit equivalent to Hermann actions

Such actions are either Hermann actions or of cohomogeneity one

Provides a classification of hyperpolar actions on reducible symmetric spaces

Abstract

We study hyperpolar actions on reducible symmetric spaces of the compact type. Our main result is that an indecomposable hyperpolar action on a symmetric space of the compact type is orbit equivalent to a Hermann action or of cohomogeneity one.