Pseudo-Riemannian almost hypercomplex homogeneous spaces with irreducible isotropy

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.

Final version. 12 pages, 1 table, no figures

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