Actions of vanishing homogeneity rank on quaternionic-Kaehler projective spaces

TL;DR

This paper classifies isometric actions of compact Lie groups on quaternionic-Kähler projective spaces with vanishing homogeneity rank, revealing their properties and showing they are generally not quaternion-coisotropic.

Contribution

It provides a complete classification of such actions and clarifies their geometric nature, which was previously not well understood.

Findings

Classified all isometric actions with vanishing homogeneity rank

Demonstrated these actions are generally not quaternion-coisotropic

Enhanced understanding of symmetry properties in quaternionic-Kähler spaces

Abstract

We classify isometric actions of compact Lie groups on quaternionic-K\"ahler projective spaces with vanishing homogeneity rank. We also show that they are not in general quaternion-coisotropic.