Some remarks on polar actions

TL;DR

This paper classifies infinitesimally polar actions on rank-one compact symmetric spaces and shows that all such polar actions share the same orbits as asystatic actions, providing insight into their structure.

Contribution

It provides a classification of infinitesimally polar actions on rank-one symmetric spaces and relates polar actions to asystatic actions.

Findings

Classified infinitesimally polar actions on rank-one symmetric spaces

Proved that polar actions have the same orbits as asystatic actions on these spaces

Abstract

We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.