Feuilletages riemanniens sur les variétés simplement connexes
Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 203-223.

Nous étudions les feuilletages riemanniens sur les variétés simplement connexes d’un point de vue qualitatif. Nous montrons tout d’abord que ces feuilletages peuvent être approchés par des fibrations de Seifert généralisées. Nous montrons ensuite que, pour une certaine métrique quasi-fibrée, les feuilles de ces feuilletages sont des sous-variétés minimales. Comme application, nous montrons que les seuls feuilletages riemanniens qui ne sont pas des fibrés de seifert, sur les sphères et les espace projectifs, sont de dimension 1.

Riemannian foliations on simply connected manifolds are studied from a qualitative point of view. We show that these foliations can be approximated by generalized Seifert fibrations. Then, we show that, for some bundle-like metric, the leaves of such foliations are minimal submanifolds. As an application, we show that the only riemannian foliations which are not Seifert fibrations, on spheres and projective spaces, are 1 dimensional.

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Ghys, Étienne. Feuilletages riemanniens sur les variétés simplement connexes. Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 203-223. doi : 10.5802/aif.994. https://www.numdam.org/articles/10.5802/aif.994/

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