Polar actions on the complex hyperbolic plane

TL;DR

This paper classifies all polar actions on the complex hyperbolic plane, identifying specific actions of various cohomogeneities, and provides a comprehensive understanding of their orbit structures.

Contribution

It offers a complete classification of polar actions on the complex hyperbolic plane, detailing their types and orbit equivalence classes.

Findings

Identified five cohomogeneity one polar actions.

Identified four cohomogeneity two polar actions.

Classified all polar actions up to orbit equivalence.

Abstract

We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.