Homogeneous polar foliations of complex hyperbolic spaces

TL;DR

This paper classifies all homogeneous polar foliations of complex hyperbolic spaces, showing there are exactly 2n+1 such foliations and providing explicit descriptions for each.

Contribution

It provides a complete classification and explicit descriptions of all homogeneous polar foliations in complex hyperbolic spaces, a previously unresolved problem.

Findings

Exactly 2n+1 homogeneous polar foliations exist in complex hyperbolic spaces.

Explicit descriptions of each of these foliations are provided.

The classification is up to isometric congruence.

Abstract

We prove that, up to isometric congruence, there are exactly 2n+1 homogeneous polar foliations of the complex hyperbolic space. We also give an explicit description of each of these foliations.