A class of Lorentzian manifolds with indecomposable holonomy groups

Details A class of Lorentzian manifolds with indecomposable holonomy groups A class of Lorentzian manifolds with indecomposable holonomy groups

2008-03-31

arxiv.org/abs/0803.4494v4

Mathematics

Differential Geometry

14 pages, minor corrections

Scientific paper

We consider a class of $S^{1}$-bundles whose total space admits a nowhere
vanishing recurrent lightlike vector field with respect to a Lorentzian metric.
This metric can be modified such that its restricted holonomy group is
indecomposable and reducible. We apply Hodge theory to construct examples with
Hermitian screen holonomy. Finally, we construct complete pp-waves.

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