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Remark on holonomy groups of pseudo-Riemannian manifolds of signature (2,n+2) | | Anton S. Galaev
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21 Jun 2004 | | Subject: | Differential Geometry MSC-class: 53B30, 53C29, 53C50 | math.DG | | Abstract: | We consider one type of weakly-irreducible not irreducible subalgebras of $so(2,n+2)$. Each Lie algebra $g^h$ of this type is uniquely defined by the associated subalgebra $hsubsetso(n)$. For any $hsubsetso(n)$ we realize $g^h$ as the holonomy algebra of a pseudo-Riemannian manifold of signature $(2,n+2)$. This shows the principal difference from the case of Lorentzian manifolds, where the analogous subalgebra $hsubsetso(n)$ associated to the holonomy algebra has to be the holonomy algebra of a Riemannian manifold. | | Source: | arXiv, math.DG/0406397 | | Services: | Forum | Review | PDF | Favorites | |
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