Transversely homogeneous foliations
Annales de l'Institut Fourier, Volume 29 (1979) no. 4, p. 143-158

A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space G/K which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when K is compact. We investigate the relationship between the structure equations of G and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special case, we study the transversely elliptic, Euclidean, and hyperbolic foliations.

Un feuilletage d’une variété s’appelle transversalement homogène s’il peut être défini par des submersions locales prenant leurs valeurs dans un espace homogène G/K telles que les changements des cartes sont des translations. Nous étudions la topologie et la géométrie de ces feuilletages et nous donnons un théorème de structure pour le cas où K est compact. Nous considérons la relation entre les équations de structure de G et l’espace fibré vectoriel transverse au feuilletage, et nous donnons une caractérisation au moyen des formes différentielles pour une grande classe des feuilletages homogènes. Enfin, nous étudions les feuilletages transversalement elliptiques, euclidiens, et hyperboliques.

@article{AIF_1979__29_4_143_0,
     author = {Blumenthal, Robert A.},
     title = {Transversely homogeneous foliations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {29},
     number = {4},
     year = {1979},
     pages = {143-158},
     doi = {10.5802/aif.771},
     mrnumber = {558593},
     zbl = {0405.57016},
     mrnumber = {81h:57011},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1979__29_4_143_0}
}
Blumenthal, Robert A. Transversely homogeneous foliations. Annales de l'Institut Fourier, Volume 29 (1979) no. 4, pp. 143-158. doi : 10.5802/aif.771. http://www.numdam.org/item/AIF_1979__29_4_143_0/

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