Geodesic
Weil foliations
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 219-231

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A foliation that admits a Weil geometry as its transverse structure is called by us a Weil foliation. We proved that there exists an attractor for any Weil foliation that is not Riemannian foliation. If such foliation is proper, there exists an attractor coincided with a closed leaf. The above assertions are proved without assumptions of compactness of foliated manifolds and completeness of the foliations. We proved also that an arbitrary complete Weil foliation either is a Riemannian foliation, with the closure of each leaf forms a minimal set, or it is a trasversally similar foliation and there exists a global attractor. Any proper complete Weil foliation either is a Riemannian foliation, with all their leaves are closed and the leaf space is a smooth orbifold, or it is a trasversally similar foliation, and it has a unique closed leaf which is a global attractor of this foliation.
Mots-clés : Weil foliation
Keywords: minimal set, attractor, holonomy group. 
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     title = {Weil foliations},
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N. I. Zhukova. Weil foliations. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 219-231. http://geodesic.mathdoc.fr/item/ND_2010_6_1_a15/