Classification of connected holonomy groups of pseudo-Kählerian manifolds of index 2

Abstract

The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreducible not irreducible subalgebras of $\su(1,n+1)$ ($n\ge 0$) are classified. Weakly-irreducible not irreducible holonomy algebras of pseudo-Kählerian and special pseudo-Kählerian manifolds are classified. An example of metric for each possible holonomy algebra is given. This gives the classification of holonomy algebras for pseudo-Kählerian manifolds of index 2

This paper has been withdrawn, since the results of this paper are obtained in a much simpler way in arXiv:1606.07701

References in corpus (4)

• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds
• Towards a classification of Lorentzian holonomy groups
• Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras
• Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups

Cited by in corpus (1)

• Weakly irreducible subgroups of $Sp(1,n+1)$