Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2
| dc.creator | Galaev, Anton S. | |
| dc.date | 2006-12-14 | |
| dc.date.accessioned | 2026-07-07T07:34:52Z | |
| dc.date.available | 2026-07-07T07:34:52Z | |
| dc.description | 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-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. Finally we consider some examples and applications. We describe examples of 4-dimensional Lie groups with left-invariant pseudo-Kählerian 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-Kählerian 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-Kählerian 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. | |
| dc.description | the corrected version of PhD thesis, Humbold University, Berlin | |
| dc.identifier | https://arxiv.org/abs/math/0612392 | |
| dc.identifier | http://arxiv.org/abs/math/0612392 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119919 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C29, 53C50, 53B30 | |
| dc.title | Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2 | |
| dc.type | text |