Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/101025
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Type: | Journal article |
Title: | Completeness of compact Lorentzian manifolds with abelian holonomy |
Author: | Leistner, T. Schliebner, D. |
Citation: | Mathematische Annalen, 2016; 364(3-4):1469-1503 |
Publisher: | Springer-Verlag |
Issue Date: | 2016 |
ISSN: | 0025-5831 1432-1807 |
Statement of Responsibility: | Thomas Leistner, Daniel Schliebner |
Abstract: | We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It is known that a compact Lorentzian manifold is geodesically complete if it is homogeneous, or has constant curvature, or admits a timelike conformal vector field. We consider certain Lorentzian manifolds with abelian holonomy, which are locally modelled by the so called pp-waves, and which, in general, do not satisfy any of the above conditions. We show that compact pp-waves are universally covered by a vector space, determine the metric on the universal cover, and prove that they are geodesically complete. Using this, we show that every Ricci-flat compact pp-wave is a plane wave. |
Rights: | © Springer-Verlag Berlin Heidelberg 2015 |
DOI: | 10.1007/s00208-015-1270-4 |
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/s00208-015-1270-4 |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
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RA_hdl_101025.pdf Restricted Access | Restricted Access | 656.44 kB | Adobe PDF | View/Open |
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