On the full holonomy group of special Lorentzian manifolds

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...

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Bibliographic Details
Published in:arXiv.org 2012-05
Main Authors: Baum, Helga, Lärz, Kordian, Leistner, Thomas
Format: Article
Language:English
Subjects:
Chemical industry
Fields (mathematics)
Hyperspaces
Manifolds (mathematics)
Quotients
Riemann manifold
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1204.5657