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- W1574209293 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 $su(1,n+1)$ ($ngeq 0$) are classified. Weakly-irreducible not irreducible holonomy algebras of pseudo-Kahlerian and special pseudo-Kahlerian manifolds are classified. An example of metric for each possible holonomy algebra is given. This gives the classification of holonomy algebras for pseudo-Kahlerian manifolds of index 2. Finally we consider some examples and applications. We describe examples of 4-dimensional Lie groups with left-invariant pseudo-Kahlerian metrics and determine their holonomy algebras. We use our classification of holonomy algebras to give a new proof for the classification of simply connected pseudo-Kahlerian symmetric spaces of index 2 with weakly-irreducible not irreducible holonomy algebras. We consider time-like cones over Lorentzian Sasaki manifolds. These cones are also pseudo-Kahlerian manifolds of index 2. We describe the local DeRham-Wu decomposition of the cone in terms of the initial Lorentzian Sasaki manifold and we describe all possible weakly-irreducible not irreducible holonomy algebras of such cones." @default.
- W1574209293 created "2016-06-24" @default.
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- W1574209293 date "2006-12-14" @default.
- W1574209293 modified "2023-09-27" @default.
- W1574209293 title "Holonomy groups and special geometric structures of pseudo-Kahlerian manifolds of index 2" @default.
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