Displaying similar documents to “Existence of foliations on 4-manifolds.”

The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev (1996)

Annales de l'institut Fourier

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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.

Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type

Hiromichi Nakayama (1991)

Annales de l'institut Fourier

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We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.

Codimension one foliations on complex tori

Marco Brunella (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

On transcendental automorphisms of algebraic foliations

B. Scárdua (2003)

Fundamenta Mathematicae

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We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation...

Numerically trivial foliations

Thomas Eckl (2004)

Annales de l’institut Fourier

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Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kähler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji’s numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic singularities on a pseudo-effective line bundle , a foliation is constructed refining the nef fibration. If the singularities of the...