Finsler Conformal Lichnerowicz-Obata conjecture
Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 937-949.

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.

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.

Received:
Accepted:
DOI: 10.5802/aif.2452
Classification: 58b20,  53c60
Keywords: Finsler metric, conformal transformation
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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Matveev, V. S.; Rademacher, H.-B.; Troyanov, M.; Zeghib, A. Finsler Conformal Lichnerowicz-Obata conjecture. Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 937-949. doi : 10.5802/aif.2452. https://aif.centre-mersenne.org/articles/10.5802/aif.2452/

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