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Regular version of the site

Article

Global attractors of complete conformal foliations

Sbornik Mathematics. 2012. Vol. 203. No. 2. P. 380-405.

We prove that every complete foliation (M, F) of codimension q > 1 is either Riemannian or a (Conf (S^q), S^q)-foliation. We further prove that if  (M, F) is not Riemannian, it has a global attractor which is either a nontrivial minimal set or a closed leaf or a union of two closed leaves. In particular, every proper conformal non-Riemannian foliation (M, F) has a global attractor which is either a closed leaf or a union of two closed leaves, and the space of all non-closed leaves is a connected q-dimensional orbifold. We show that every countable group of conformal transformations of the sphere S^q can be realized as a global holonomy group of complete conformal foliation. Examples of complete conformal foliations with exceptional and exotic minimal sets as global attractors are constructed.