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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Affine transformations and parallel lightlike vector fields on compact Lorentzian 3-manifolds

Authors: Charles Boubel and Pierre Mounoud
Journal: Trans. Amer. Math. Soc. 368 (2016), 2223-2262
MSC (2010): Primary 53C29, 53C50
Published electronically: July 10, 2015
MathSciNet review: 3449238
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Abstract: We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting nonisometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivariant deformation of a flat one.

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Charles Boubel
Affiliation: Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
MR Author ID: 684179

Pierre Mounoud
Affiliation: Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux et CNRS, 351, cours de la libération, F-33405 Talence, France
MR Author ID: 681800

Received by editor(s): April 17, 2014
Received by editor(s) in revised form: November 24, 2014
Published electronically: July 10, 2015
Article copyright: © Copyright 2015 American Mathematical Society