Feuilletages transversalement projectifs sur les variétés de Seifert  [ Transversely projective foliations on Seifert manifolds ]
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, p. 1551-1613

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.

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.

DOI : https://doi.org/10.5802/aif.1988
Classification:  57M50,  57R30,  37D40
Keywords: transversely projective foliations, Seifert manifolds
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     author = {Barbot, Thierry},
     title = {Feuilletages transversalement projectifs sur les vari\'et\'es de Seifert},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {5},
     year = {2003},
     pages = {1551-1613},
     doi = {10.5802/aif.1988},
     zbl = {1036.57006},
     mrnumber = {2032943},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2003__53_5_1551_0}
}
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. http://www.numdam.org/item/AIF_2003__53_5_1551_0/

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