Self Dual Einstein Orbifolds with Few Symmetries as Quaternion Kaehler Quotients

TL;DR

This paper constructs new compact orbifolds with special geometric properties, classifies all such 4-dimensional quaternion Kähler quotients by tori, and enhances understanding of their symmetry and structure.

Contribution

It introduces a new family of self-dual Einstein orbifolds with minimal symmetries and completes the classification of 4D quaternion Kähler torus quotients of Grassmannians.

Findings

Constructed a new family of compact orbifolds with positive self-dual Einstein metrics.

Classified all 4D quaternion Kähler orbifolds obtained as torus quotients of Grassmannians.

Identified the symmetry properties of these orbifolds, showing they have minimal isometry groups.

Abstract

We construct a new family of compact orbifolds with a positive self dual Einstein metric and a one-dimensional group of isometries. Together with another known family, these examples classify all 4-dimensional orbifolds that are quaternion Kaehler quotients by a torus of real Grassmannians.