In this article we prove that every conformal foliation, transversely analytic, of codimension at most three on a compact connected manifold is either transversely Möbius or Riemannian. This theorem can be seen as a generalisation of the Ferrand-Obata theorem transversely to a foliation.
Dans cet article nous montrons que tout feuilletage conforme, transversalement analytique, de codimension supérieure ou égale à trois sur une variété compacte connexe est transversalement Möbius ou riemannien. Ce théorème peut être vu comme une généralisation, transversalement à un feuilletage, du théorème Ferrand-Obata.
Mot clés : feuilletages, pseudogroupes, géométrie différentielle conforme.
Keywords: foliations, pseudogroups, conformal differential geometry.
@article{AIF_2004__54_2_453_0, author = {Tarquini, C\'edric}, title = {Feuilletages conformes}, journal = {Annales de l'Institut Fourier}, pages = {453--480}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {2}, year = {2004}, doi = {10.5802/aif.2025}, zbl = {1064.53014}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2025/} }
TY - JOUR AU - Tarquini, Cédric TI - Feuilletages conformes JO - Annales de l'Institut Fourier PY - 2004 SP - 453 EP - 480 VL - 54 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2025/ DO - 10.5802/aif.2025 LA - fr ID - AIF_2004__54_2_453_0 ER -
Tarquini, Cédric. Feuilletages conformes. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 453-480. doi : 10.5802/aif.2025. http://archive.numdam.org/articles/10.5802/aif.2025/
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