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Holonomy Groups of Lorentzian Manifolds: A Status Report

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Global Differential Geometry

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 17))

Abstract

In this survey we review the state of art in Lorentzian holonomy theory. We explain the recently completed classification of connected Lorentzian holonomy groups, we describe local and global metrics with special Lorentzian holonomy and some topological properties, and we discuss the holonomy groups of Lorentzian manifolds with parallel spinors as well as Lorentzian Einstein metrics with special holonomy.

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  1. Institut für Mathematik, Humboldt Universität Berlin, Sitz: Rudower Chaussee 25, 12489, Berlin, Germany

    Helga Baum

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  1. Helga Baum
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Correspondence to Helga Baum .

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  1. Inst. Mathematik, Universität Potsdam, Potsdam, Brandenburg, Germany

    Christian Bär

  2. , Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster, 48149, Germany

    Joachim Lohkamp

  3. , Fakultät für Mathematik und Informatik, Universität Leipzig, Johannisgasse 26, Leipzig, 04103, Sachsen, Germany

    Matthias Schwarz

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Baum, H. (2012). Holonomy Groups of Lorentzian Manifolds: A Status Report. In: Bär, C., Lohkamp, J., Schwarz, M. (eds) Global Differential Geometry. Springer Proceedings in Mathematics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22842-1_7

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