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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
DOI: https://doi.org/10.1090/tran/6645
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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Additional Information

Charles Boubel
Affiliation: Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: charles.boubel@unistra.fr

Pierre Mounoud
Affiliation: Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux et CNRS, 351, cours de la libération, F-33405 Talence, France
Email: pierre.mounoud@math.u-bordeaux1.fr

DOI: https://doi.org/10.1090/tran/6645
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

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