Metrics that realize all Lorentzian holonomy algebras

Details Metrics that realize all Lorentzian holonomy algebras Metrics that realize all Lorentzian holonomy algebras

2005-02-28

arxiv.org/abs/math/0502575v2

Int. J. Geom. Methods Mod. Phys. 3 (2006) no. 5-6, 1025--1045

Mathematics

Differential Geometry

Scientific paper

All candidates to the weakly-irreducible not irreducible holonomy algebras of Lorentzian manifolds are known. In the present paper metrics that realize all these candidates as holonomy algebras are given. This completes the classification of the Lorentzian holonomy algebras. Also new examples of metrics with the holonomy algebras $g_2\zr\Real^7\subset\so(1,8)$ and $\spin(7)\zr\Real^8\subset\so(1,9)$ are constructed.

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