Structure of leaves and the complex Kupka-Smale property

Tanya Firsova

Displaying similar documents to “Structure of leaves and the complex Kupka-Smale property”

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

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The notion of the Hausdorffized leaf space $\tilde{}$ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to $\tilde{}$ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to $\tilde{}$ is shown. Finally, some examples are examined.

Foliations by complex manifolds involving the complex Hessian

Julian Ławrynowicz, Jerzy Kalina, Masami Okada

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SummaryIn 1979 the second named author proved, in a joint paper with J. Ławrynowicz, the existence of a foliation of a bounded domain in $ℂ^{n}$ by complex submanifolds of codimension k+p-1, connected in some sense with a real (1,1) C³-form of rank k and the pth power of the complex Hessian of a C³-function u with im u plurisubharmonic and the property that for every leaf of this foliation the restricted functions im u, re u and $(\partial / \partial z_{j}) i m u$ , $(\partial / \partial z_{j}) r e u$ are pluriharmonic and holomorphic, respectively.Now the...

Foliations with complex leaves

Giuliana Gigante, Giuseppe Tomassini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $X$ be a smooth foliation with complex leaves and let $D$ be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space $(X, D)$ . In particular we concentrate on the following two themes: function theory for the algebra $D (X)$ and cohomology with values in $D$ .

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....

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

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It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_{G}$ . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^{r}$ diffeomorphism group G is simple iff the foliation $ℱ_{[G, G]}$ defined by [G,G] admits no proper...

Foliations and spinnable structures on manifolds

Itiro Tamura (1973)

Annales de l'institut Fourier

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In this paper we study a new structure, called a spinnable structure, on a differentiable manifold. Roughly speaking, a differentiable manifold is spinnable if it can spin around a codimension 2 submanifold, called the axis, as if the top spins. The main result is the following: let $M$ be a compact $(n - 1)$ -connected $(2 n + 1)$ -dimensional differentiable manifold $(n \geq 3)$ , then $M$ admits a spinnable structure with axis $S^{2 n + 1}$ . Making use of the codimension-one foliation on $S^{2 n + 1}$ , this yields that $M$ admits...

A note on projective Levi flats and minimal sets of algebraic foliations

Alcides Lins Neto (1999)

Annales de l'institut Fourier

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In this paper we prove that holomorphic codimension one singular foliations on $ℂ ℙ^{n}, n \geq 3$ have no non trivial minimal sets. We prove also that for $n \geq 3$ , there is no real analytic Levi flat hypersurface in $ℂ ℙ^{n}$ .

On deformations of holomorphic foliations

Joan Girbau, Marcel Nicolau (1989)

Annales de l'institut Fourier

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Given a non-singular holomorphic foliation $ℱ$ on a compact manifold $M$ we analyze the relationship between the versal spaces $K$ and $K^{tr}$ of deformations of $ℱ$ as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of $ℱ$ parametrized by an analytic space $K^{f}$ isomorphic to $π^{- 1} (0) \times Σ$ where $Σ$ is smooth and $π$ : $K \to K^{tr}$ is the forgetful map. The map $π$ is shown to be an epimorphism in two situations: (i) if $H^{2} (M, Θ_{ℱ}^{f}) = 0$ , where $Θ_{ℱ}^{f}$ is...

Taut foliations of 3-manifolds and suspensions of $S^{1}$

David Gabai (1992)

Annales de l'institut Fourier

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Let $M$ be a compact oriented 3-manifold whose boundary contains a single torus $P$ and let $ℱ$ be a taut foliation on $M$ whose restriction to $\partial M$ has a Reeb component. The main technical result of the paper, asserts that if $N$ is obtained by Dehn filling $P$ along any curve not parallel to the Reeb component, then $N$ has a taut foliation.