Isometric actions on spheres with an orbifold quotient

TL;DR

This paper classifies certain group actions on spheres where the quotient space forms a Riemannian orbifold, advancing understanding of symmetries and geometric structures in orbifold theory.

Contribution

It provides a complete classification of representations of compact connected Lie groups with orbifold quotient actions on spheres, a novel result in geometric group actions.

Findings

Classification of Lie group representations with orbifold quotients

Identification of conditions for isometric orbifold quotients

Extension of orbifold symmetry understanding in geometric analysis

Abstract

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.