Quaternionic geometry in dimension eight

TL;DR

This paper explores 8-dimensional Wolf spaces as SU(3)-manifolds, and finds new quaternionic metrics on G_2/SO(4) that are not Einstein but have closed fundamental 4-forms.

Contribution

It provides a new geometric description of Wolf spaces and introduces non-Einstein quaternionic metrics with closed 4-forms on G_2/SO(4).

Findings

Wolf spaces as cohomogeneity one SU(3)-manifolds

Perturbations of quaternion-Kähler metrics on G_2/SO(4)

Existence of non-Einstein metrics with closed 4-forms

Abstract

We describe the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental 4-form but are not Einstein.