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.
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/} }
TY - JOUR AU - Matveev, V. S. AU - Rademacher, H.-B. AU - Troyanov, M. AU - Zeghib, A. TI - Finsler Conformal Lichnerowicz-Obata conjecture JO - Annales de l'Institut Fourier PY - 2009 DA - 2009/// SP - 937 EP - 949 VL - 59 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2452/ UR - https://www.ams.org/mathscinet-getitem?mr=2543657 UR - https://zbmath.org/?q=an%3A1179.53075 UR - https://doi.org/10.5802/aif.2452 DO - 10.5802/aif.2452 LA - en ID - AIF_2009__59_3_937_0 ER -
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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