Screen bundles of Lorentzian manifolds and some generalisations of pp-waves

Details Screen bundles of Lorentzian manifolds and some generalisations of pp-waves Screen bundles of Lorentzian manifolds and some generalisations of pp-waves

2005-07-04

arxiv.org/abs/math/0507048v1

Mathematics

Differential Geometry

18 pages

Scientific paper

10.1016/j.geomphys.2005.11.010

A pp-wave is a Lorentzian manifold with a parallel light-like vector field satisfying a certain curvature condition. We introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. These generalisations are related to the screen holonomy of the Lorentzian manifold. While pp-waves have a trivial screen holonomy there are no restrictions on the screen holonomy of the manifolds with the weaker curvature condition.

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