Let be a Seifert manifold with non-solvable fundamental group. Let be a one- dimensional foliation on , equipped with a transverse real projective structure. We assume moreover that satisfies the Homotopy Lifting Property, i.e., that the leaf space of the lifting of in the universal covering of satisfies the Hausdorff separation property. Then, up to finite coverings, belongs to one of the following three families of transversely projective foliations: the family of projective fibrations, the family of convex geodesic foliations, or the family of projective horocyclic foliations.
Soit une variété de Seifert de groupe fondamental non virtuellement résoluble. Soit un feuilletage de dimension sur , muni d’une structure projective réelle transverse. On suppose que satisfait la propriété de relèvement des chemins, i.e., que l’espace des feuilles du relèvement de dans le revêtement universel de est séparé au sens de Hausdorff. On montre qu’à revêtements finis près, est soit une fibration projective, soit un feuilletage géodésique convexe, soit un feuilletage horocyclique projectif.
Mot clés : feuilletage transversalement projectif, variété de Seifert
Keywords: transversely projective foliations, Seifert manifolds
Barbot, Thierry 1
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TY - JOUR AU - Barbot, Thierry TI - Feuilletages transversalement projectifs sur les variétés de Seifert JO - Annales de l'Institut Fourier PY - 2003 SP - 1551 EP - 1613 VL - 53 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1988/ DO - 10.5802/aif.1988 LA - fr ID - AIF_2003__53_5_1551_0 ER -
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Barbot, Thierry. Feuilletages transversalement projectifs sur les variétés de Seifert. Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1551-1613. doi : 10.5802/aif.1988. https://aif.centre-mersenne.org/articles/10.5802/aif.1988/
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