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Lorentzian foliations on 3-manifolds

Published online by Cambridge University Press:  11 September 2006

C. BOUBEL ,
P. MOUNOUD  and
C. TARQUINI
C. BOUBEL
Affiliation:
École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, 46 allée d'Italie, F-69364 Lyon Cedex 07, France (e-mail: charles.boubel@ens-lyon.fr, cedric.tarquini@ens-lyon.fr)
P. MOUNOUD
Affiliation:
Université Bordeaux 1, Laboratoire Bordelais d'Analyse et Géométrie, 351 cours de la Libération, F-33405 Talence Cedex, France (e-mail: pierre.mounoud@math.u-bordeaux1.fr)
C. TARQUINI
Affiliation:
École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, 46 allée d'Italie, F-69364 Lyon Cedex 07, France (e-mail: charles.boubel@ens-lyon.fr, cedric.tarquini@ens-lyon.fr)
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Abstract

We study transversely Lorentzian foliations of closed 3-manifolds. We classify them under a completeness hypothesis and deduce the dual classification of codimension-one geodesically complete timelike totally geodesic foliations. Also we provide an example of a Lorentzian foliation of a compact 3-manifold which is equicontinuous on a proper dense open subset of the manifold, and hence not transversely complete.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1339 - 1362
Copyright
2006 Cambridge University Press

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