Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/101083
Citations | ||
Scopus | Web of Science® | Altmetric |
---|---|---|
?
|
?
|
Type: | Journal article |
Title: | On the full holonomy group of Lorentzian manifolds |
Author: | Baum, H. Lärz, K. Leistner, T. |
Citation: | Mathematische Zeitschrift, 2014; 277(3-4):797-828 |
Publisher: | Springer-Verlag |
Issue Date: | 2014 |
ISSN: | 0025-5874 1432-1823 |
Statement of Responsibility: | Helga Baum, Kordian Lärz, Thomas Leistner |
Abstract: | The classification of restricted holonomy groups of n-dimensional Lorentzian manifolds was obtained about ten years ago. However, up to now, not much is known about the structure of the full holonomy group. In this paper we study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. Based on the classification of the restricted holonomy groups of such manifolds, we prove several structure results about the full holonomy. We establish a construction method for manifolds with disconnected holonomy starting from a Riemannian manifold and a properly discontinuous group of isometries. This leads to a variety of examples, most of them being quotients of pp-waves with disconnected holonomy, including a non-flat Lorentzian manifold with infinitely generated holonomy group. 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. |
Keywords: | Lorentzian manifolds; Holonomy groups; Isometry groups; Parallel spinor fields Globally hyperbolic manifolds, pp-waves |
Rights: | © Springer-Verlag Berlin Heidelberg 2014 |
DOI: | 10.1007/s00209-014-1279-5 |
Grant ID: | http://purl.org/au-research/grants/arc/FT110100429 http://purl.org/au-research/grants/arc/DP120104582 |
Published version: | http://dx.doi.org/10.1007/s00209-014-1279-5 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.