Foliations with complex leaves

Giuliana Gigante; Giuseppe Tomassini

Displaying similar documents to “Foliations with complex leaves”

Structure of leaves and the complex Kupka-Smale property

Tanya Firsova (2013)

Annales de l’institut Fourier

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We study topology of leaves of $1$ -dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.

A few remarks on the geometry of the space of leaf closures of a Riemannian foliation

Małgorzata Józefowicz, R. Wolak (2007)

Banach Center Publications

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The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in $ℝ^{k}$ for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space....

Tischler fibrations of open foliated sets

John Cantwell, Lawrence Conlon (1981)

Annales de l'institut Fourier

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Let $M$ be a closed, foliated manifold, and let $U$ be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which $U$ admits an approximating (Tischler) fibration over $S^{1}$ . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.

A note on codimension-1 foliations

Carlo Petronio (1999)

Rendiconti del Seminario Matematico della Università di Padova

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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.

Complex Analytic Realization of Reeb's Foliation of S3.

David E. Barrett (1990)

Mathematische Zeitschrift

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A foliation of $𝐑^{3}$ and other punctured 3-manifolds by circles

Elmar Vogt (1989)

Publications Mathématiques de l'IHÉS

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Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, $C^{2}$ -foliated manifolds of codimension one, having all leaves proper, are shown to be $C^{\infty}$ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class $C^{\infty}$ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class $C^{r}$ and of class $C^{r + 1}$ for every nonnegative integer $r$ .