Finsler Conformal Lichnerowicz-Obata conjecture
[La conjecture de Lichnerowicz-Obata sur les transformations conformes des variétés Finslériennes]
Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 937-949.

Nous démontrons une variante de la conjecture de Lichnerowicz-Obata sur les transformations conformes des variétés finslériennes. Plus précisément, un champ de vecteurs conforme complet et essentiel sur une variété finslérienne non-riemannienne, est un champ homothétique sur un espace vectoriel normé.

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

DOI : 10.5802/aif.2452
Classification : 58b20, 53c60
Keywords: Finsler metric, conformal transformation
Mot clés : métrique finslérienne, transformation conforme
Matveev, V. S. 1 ; Rademacher, H.-B. 2 ; Troyanov, M. 3 ; Zeghib, A. 4

1 Mathematisches Institut, Friedrich-Schiller Universität Jena 07737 Jena (Germany)
2 Mathematisches Institut, Universität Leipzig, 04081 Leipzig (Germany)
3 Section de Mathématiques, École Polytechnique Fédérale de Lausanne 1015 Lausanne (Switzerland)
4 UMPA, ENS-Lyon, 46, allée d’Italie, 69364 Lyon Cedex 07 (France)
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     title = {Finsler {Conformal} {Lichnerowicz-Obata} conjecture},
     journal = {Annales de l'Institut Fourier},
     pages = {937--949},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Matveev, V. S.; Rademacher, H.-B.; Troyanov, M.; Zeghib, A. Finsler Conformal Lichnerowicz-Obata conjecture. Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 937-949. doi : 10.5802/aif.2452. http://www.numdam.org/articles/10.5802/aif.2452/

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