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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Affine transformations and parallel lightlike vector fields on compact Lorentzian 3-manifolds
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by Charles Boubel and Pierre Mounoud PDF
Trans. Amer. Math. Soc. 368 (2016), 2223-2262 Request permission


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
  • MR Author ID: 684179
  • Email:
  • 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
  • Email:
  • Received by editor(s): April 17, 2014
  • Received by editor(s) in revised form: November 24, 2014
  • Published electronically: July 10, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 2223-2262
  • MSC (2010): Primary 53C29, 53C50
  • DOI:
  • MathSciNet review: 3449238