Hyperpolar homogeneous foliations on symmetric spaces of noncompact type

TL;DR

This paper classifies hyperpolar homogeneous foliations on all Riemannian symmetric spaces of noncompact type, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of hyperpolar homogeneous foliations on symmetric spaces of noncompact type, a problem previously unresolved.

Findings

Complete classification of hyperpolar homogeneous foliations

Identification of flat sections intersecting leaves orthogonally

Structural insights into foliations on symmetric spaces

Abstract

A foliation on a Riemannian manifold is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold that intersects each leaf of the foliation orthogonally. In this article we classify the hyperpolar homogeneous foliations on every Riemannian symmetric space of noncompact type.