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
vicente.cortes@uni-hamburg.de
Benedict Meinke
Department of Mathematics, University of Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
Benedict.Meinke@uni-duesseldorf.de
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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