Volume 17, issue 1 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Sur les surfaces lorentziennes compactes sans points conjugués

Christophe Bavard and Pierre Mounoud

Geometry & Topology 17 (2013) 469–492
Abstract

Nous prouvons l’existence de métriques sans points conjugués dans toute composante connexe de l’espace des métriques lorentziennes du tore ou de la bouteille de Klein. En particulier, l’existence de tores lorentziens sans points conjugués non plats contraste avec la situation riemannienne (théorème de Hopf).

We prove the existence of metrics without conjugate points in any connected component of the space of Lorentzian metrics on the torus or on the Klein bottle. In particular, the existence of nonflat Lorentzian tori without conjugate points contrasts with the Riemannian case (the Hopf Theorem).

Keywords
Lorentzian surfaces, conjugate points, surfaces lorentziennes, points conjugués
Mathematical Subject Classification 2010
Primary: 53C50
References
Publication
Received: 30 May 2011
Revised: 8 October 2012
Accepted: 3 July 2012
Published: 23 March 2013
Proposed: Jean-Pierre Otal
Seconded: Yasha Eliashberg, Dmitri Burago
Authors
Christophe Bavard
Institut de Mathématiques de Bordeaux
Université Bordeaux 1
351 cours de la Libération
33405 Talence
France
Pierre Mounoud
Institut de Mathématiques de Bordeaux
Université Bordeaux 1
351 cours de la Libération
33405 Talence
France