Codimension two polar homogeneous foliations on symmetric spaces of noncompact type

TL;DR

This paper classifies codimension two homogeneous polar foliations on irreducible noncompact symmetric spaces, showing they are either hyperpolar or derived from rank one spaces, advancing understanding of geometric structures in these spaces.

Contribution

It provides a complete classification of such foliations, identifying their types and relation to rank one symmetric spaces, which was previously unknown.

Findings

All codimension two homogeneous polar foliations are either hyperpolar or canonical extensions from rank one spaces.

The classification is up to orbit equivalence, providing a comprehensive understanding of these foliations.

The results unify the structure of polar foliations on noncompact symmetric spaces.

Abstract

We classify homogeneous polar foliations of codimension two on irreducible symmetric spaces of noncompact type up to orbit equivalence. Any such foliation is either hyperpolar or the canonical extension of a polar homogeneous foliation on a rank one symmetric space.