Lightlike foliations on Lorentzian manifolds with weakly irreducible holonomy algebra

Details Lightlike foliations on Lorentzian manifolds with weakly irreducible holonomy algebra Lightlike foliations on Lorentzian manifolds with weakly irreducible holonomy algebra

2005-06-06

arxiv.org/abs/math/0506101v1

Mathematics

Differential Geometry

18 pages

Scientific paper

We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one lightlike hypersurface. This gives us some global operators on the manifold. Using these operators, we decompose the curvature tensor of the manifold into several components. We give a criteria how to find the type of the holonomy algebras (there are 4 possible types) in terms of the global operators.

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