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arXiv · 1204.5657

On the full holonomy group of special Lorentzian manifolds

Helga Baum·Kordian Lärz·Thomas Leistner
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Abstract

We study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. We prove several results that are based on the classification of the restricted holonomy groups of such manifolds and provide a construction method for manifolds with disconnected holonomy which starts from a Riemannian manifold and a properly discontinuous group of isometries. Most of our examples are quotients of pp-waves with disconnected holonomy and without parallel vector field. Furthermore, we classify the full holonomy groups of solvable Lorentzian symmetric spaces and of Lorentzian manifolds with a parallel null spinor. Finally, we construct examples of globally hyperbolic manifolds with complete spacelike Cauchy hypersurfaces, disconnected full holonomy and a parallel spinor.

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Helga Baum, Kordian Lärz, Thomas Leistner. 2012-05-15. On the full holonomy group of special Lorentzian manifolds. https://doi.org/10.1007/s00209-014-1279-5

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