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Journal of Lie Theory 27 (2017), No. 4, 982--993
Copyright Heldermann Verlag 2017

Pseudo-Riemannian Almost Hypercomplex Homogeneous Spaces with Irreducible Isotropy

Vicente Cortés
Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany

Benedict Meinke
Department of Mathematics, University of Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany

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 hyper-Kähler and flat except in dimension 12.

Keywords: Homogeneous spaces, symmetric spaces, almost hypercomplex structures, pseudo-Riemannian manifolds.

MSC: 53C26, 53C30, 53C35, 53C50

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