Impact Factor

    Weil foliations

    2010, Vol. 6, No. 1, pp.  219-231

    Author(s): Zhukova N. I.

    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.
    Keywords: Weil foliation, minimal set, attractor, holonomy group
    Citation: Zhukova N. I., Weil foliations, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 1, pp.  219-231

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