no. 3

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 : https://doi.org/10.5802/aif.2452
Classification : 58b20,  53c60
Mots clés : métrique finslérienne, transformation conforme 
@article{AIF_2009__59_3_937_0,
     author = {Matveev, V. S. and Rademacher, H.-B. and Troyanov, M. and Zeghib, A.},
     title = {Finsler Conformal Lichnerowicz-Obata conjecture},
     journal = {Annales de l'Institut Fourier},
     pages = {937--949},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {3},
     year = {2009},
     doi = {10.5802/aif.2452},
     mrnumber = {2543657},
     zbl = {1179.53075},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2452/}
}
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://archive.numdam.org/articles/10.5802/aif.2452/

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