Feuilletages transversalement projectifs sur les variétés de Seifert
Barbot, Thierry
Annales de l'Institut Fourier, Tome 53 (2003), p. 1551-1613 / Harvested from Numdam
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Soit M une variété de Seifert de groupe fondamental non virtuellement résoluble. Soit Φ un feuilletage de dimension 1 sur M, muni d’une structure projective réelle transverse. On suppose que Φ satisfait la propriété de relèvement des chemins, i.e., que l’espace des feuilles du relèvement de Φ dans le revêtement universel de M est séparé au sens de Hausdorff. On montre qu’à revêtements finis près, Φ est soit une fibration projective, soit un feuilletage géodésique convexe, soit un feuilletage horocyclique projectif.

Let M be a Seifert manifold with non-solvable fundamental group. Let Φ be a one- dimensional foliation on M, equipped with a transverse real projective structure. We assume moreover that Φ satisfies the Homotopy Lifting Property, i.e., that the leaf space of the lifting of Φ in the universal covering of M satisfies the Hausdorff separation property. Then, up to finite coverings, Φ 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.

Publié le : 2003-01-01
DOI : https://doi.org/10.5802/aif.1988
Classification:  57M50,  57R30,  37D40
Mots clés: feuilletage transversalement projectif, variété de Seifert 
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     title = {Feuilletages transversalement projectifs sur les vari\'et\'es de Seifert},
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     doi = {10.5802/aif.1988},
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Barbot, Thierry. Feuilletages transversalement projectifs sur les variétés de Seifert. Annales de l'Institut Fourier, Tome 53 (2003) pp. 1551-1613. doi : 10.5802/aif.1988. http://gdmltest.u-ga.fr/item/AIF_2003__53_5_1551_0/

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