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

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

2004-05-06

arxiv.org/abs/math/0405098v4

Mathematics

Differential Geometry

Scientific paper

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 $\su(1,n+1)$ ($n\geq 0$) are classified. Weakly-irreducible not irreducible holonomy algebras of pseudo-K\"ahlerian and special pseudo-K\"ahlerian manifolds are classified. An example of metric for each possible holonomy algebra is given. This gives the classification of holonomy algebras for pseudo-K\"ahlerian manifolds of index 2

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