Finsler Conformal Lichnerowicz-Obata conjecture

Matveev, V. S.; Rademacher, H.-B.; Troyanov, M.; Zeghib, A.

doi:10.5802/aif.2452

Finsler Conformal Lichnerowicz-Obata conjecture
[La conjecture de Lichnerowicz-Obata sur les transformations conformes des variétés Finslériennes]

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)

Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 937-949.

Résumé
Abstract

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.

MR Zbl

DOI : 10.5802/aif.2452

Classification : 58b20, 53c60
Keywords: Finsler metric, conformal transformation
Mot clés : métrique finslérienne, transformation conforme

Affiliations des auteurs :

Matveev, V. S. ¹ ; Rademacher, H.-B. ² ; Troyanov, M. ³ ; Zeghib, A. ⁴

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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},
     volume = {59},
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     url = {http://www.numdam.org/articles/10.5802/aif.2452/}
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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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