Cet article concerne les flots projectivement Anosov, dont les feuilletages stable et instable et sont lisses, sur une variété de Seifert . Nous prouvons que si l’un des feuilletages ou contient une feuille compacte, alors le flot se décompose en union finie de modèles définis sur et ayant pour bord les feuilles compactes. La variété est donc homeomorphe au tore . Dans la preuve, nous obtenons également un théorème qui classifie les feuilletages de codimension un sur les variétés de Seifert ayant des feuilles compactes qui sont des tores incompressibles.
This paper concerns projectively Anosov flows with smooth stable and unstable foliations and on a Seifert manifold . We show that if the foliation or contains a compact leaf, then the flow is decomposed into a finite union of models which are defined on and bounded by compact leaves, and therefore the manifold is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible tori.
Classification : 57R30, 37D30, 53C12, 53C15
Mots clés : flots projectivement Anosov, feuilletages stables, structures de bi-contact
@article{AIF_2004__54_2_481_0, author = {Noda, Takeo}, title = {Regular projectively Anosov flows with compact leaves}, journal = {Annales de l'Institut Fourier}, pages = {481--497}, publisher = {Association des Annales de l'institut Fourier}, volume = {54}, number = {2}, year = {2004}, doi = {10.5802/aif.2026}, zbl = {1058.57021}, language = {en}, url = {www.numdam.org/item/AIF_2004__54_2_481_0/} }
Noda, Takeo. Regular projectively Anosov flows with compact leaves. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 481-497. doi : 10.5802/aif.2026. http://www.numdam.org/item/AIF_2004__54_2_481_0/
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