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Metrics that realize all types of Lorentzian holonomy algebras | | Anton S. Galaev
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28 Feb 2005 | | Subject: | Differential Geometry MSC-class: 53C29, 53C50, 53B30 | math.DG | | Abstract: | The holonomy algebra of an indecomposable (n+2)-dimensional Lorentzian manifold $M$ is a weakly-irreducible subalgebra of the Lorentzian algebra $so(1,n+1)$. L. Berard Bergery and A. Ikemakhen divided weakly-irreducible not irreducible subalgebras $gsubsetso(1,n+1)$ into 4 types and associated with each such subalgebra $g$ a subalgebra $hsubset so(n)$. T. Leistner proved that the subalgebra $hsubsetso(n)$ associated to a holonomy algebra is the holonomy algebra of a Riemannian manifold. Before there were known metrics that realize all weakly-irreducible not irreducible algebras of type 1 and 2 with any associated holonomy algebra of a Riemannian manifold. In the present paper we construct such metrics for all algebras of type 3 and 4. This completes the classification of holonomy algebras for Lorentzian manifolds. | | Source: | arXiv, math.DG/0502575 | | Services: | Forum | Review | PDF | Favorites | |
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