A class of Lorentzian manifolds with indecomposable holonomy groups

Kordian Lärz

Published 2008-03-31, updated 2010-10-11Version 4

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.