Polar actions on certain principal bundles over symmetric spaces of compact type

TL;DR

This paper classifies polar actions with horizontal sections on principal bundles over compact symmetric spaces, revealing new hyperpolar actions on non-symmetric, nonnegatively curved homogeneous spaces.

Contribution

It provides a classification of polar actions on certain principal bundles and introduces examples of hyperpolar actions on non-symmetric spaces.

Findings

Classification of polar actions up to orbit equivalence.

Existence of hyperpolar actions with cohomogeneity > 1 on non-symmetric spaces.

Examples of non-symmetric, nonnegatively curved homogeneous spaces with hyperpolar actions.

Abstract

We study polar actions with horizontal sections on the total space of certain principal bundles $G/K\to G/H$ with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.