Pseudo-Riemannian almost hypercomplex homogeneous spaces with irreducible isotropy

TL;DR

This paper classifies certain 4-index pseudo-Riemannian homogeneous spaces with hypercomplex structures, finding most are flat except in 12 dimensions, advancing understanding of geometric structures with irreducible isotropy.

Contribution

It provides a classification of pseudo-Riemannian homogeneous spaces with hypercomplex structures and irreducible isotropy, identifying flatness in all but 12-dimensional cases.

Findings

All classified spaces are flat except in dimension 12.

The spaces admit invariant almost hyper-Hermitian structures.

The isotropy group is irreducible in the classified cases.

Abstract

We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are flat except in dimension 12.