Warped compact foliations

Szymon M. Walczak

Displaying similar documents to “Warped compact foliations”

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

Similarity:

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...

Minimal, rigid foliations by curves on $ℂ ℙ^{n}$

Frank Loray, Julio C. Rebelo (2003)

Journal of the European Mathematical Society

Similarity:

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space $ℂ ℙ^{n}$ for every dimension $n \geq 2$ and every degree $d \geq 2$ . Precisely, we construct a foliation $ℱ$ which is induced by a homogeneous vector field of degree $d$ , has a finite singular set and all the regular leaves are dense in the whole of $ℂ ℙ^{n}$ . Moreover, $ℱ$ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if $ℱ$ is conjugate to another holomorphic...

Foliations by complex manifolds involving the complex Hessian

Julian Ławrynowicz, Jerzy Kalina, Masami Okada

Similarity:

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...

Groups of $C^{r, s}$ -diffeomorphisms related to a foliation

Jacek Lech, Tomasz Rybicki (2007)

Banach Center Publications

Similarity:

The notion of a $C^{r, s}$ -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of $C^{r, s}$ -diffeomorphisms is proved. A remark on $C^{n + 1}$ -diffeomorphisms is given.

Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier

Similarity:

We show that any transversally complete Riemannian foliation $ℱ$ of dimension one on any possibly non-compact manifold $M$ is tense; namely, $M$ admits a Riemannian metric such that the mean curvature form of $ℱ$ is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize...

Foliations by curves with curves as singularities

M. Corrêa Jr, A. Fernández-Pérez, G. Nonato Costa, R. Vidal Martins (2014)

Annales de l’institut Fourier

Similarity:

Let $ℱ$ be a holomorphic one-dimensional foliation on $ℙ^{n}$ such that the components of its singular locus $Σ$ are curves $C_{i}$ and points $p_{j}$ . We determine the number of $p_{j}$ , counted with multiplicities, in terms of invariants of $ℱ$ and $C_{i}$ , assuming that $ℱ$ is special along the $C_{i}$ . Allowing just one nonzero dimensional component on $Σ$ , we also prove results on when the foliation happens to be determined by its singular locus.

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

Similarity:

Let $X$ be a normal projective variety, and let $A$ be an ample Cartier divisor on $X$ . Suppose that $X$ is not the projective space. We prove that the twisted cotangent sheaf $Ω_{X} \otimes A$ is generically nef with respect to the polarisation $A$ . As an application we prove a Kobayashi-Ochiai theorem for foliations: if $ℱ ⊊ T_{X}$ is a foliation such that $det ℱ \equiv i_{ℱ} A$ , then $i_{ℱ}$ is at most the rank of $ℱ$ .

A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Paolo Piccinni (1984)

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

Similarity:

Si considera la seconda forma fondamentale $\alpha$ di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano $\nabla^{2}\alpha$ - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.

Flat 3-webs of degree one on the projective plane

A. Beltrán, M. Falla Luza, D. Marín (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

The aim of this work is to study global $3$ -webs with vanishing curvature. We wish to investigate degree $3$ foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree $3$ foliations whose Legendre transform are webs with zero curvature.

Natural liftings of foliations to the $r$ -tangent bunde

Mikulski, Włodzimierz M.

Similarity:

Let $F$ be a $p$ -dimensional foliation on an $n$ -manifold $M$ , and $T^{r} M$ the $r$ -tangent bundle of $M$ . The purpose of this paper is to present some reltionship between the foliation $F$ and a natural lifting of $F$ to the bundle $T^{r} M$ . Let $L_{q}^{r} (F)$ $(q = 0, 1, \dots, r)$ be a foliation on $T^{r} M$ projectable onto $F$ and $L_{q}^{r} = {L_{q}^{r} (F)}$ a natural lifting of foliations to $T^{r} M$ . The author proves the following theorem: Any natural lifting of foliations to the $r$ -tangent bundle is equal to one of the liftings $L_{0}^{r}, L_{1}^{r}, \dots, L_{n}^{r}$ . The exposition is clear and well organized. ...

Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

The second order transverse bundle $T_{}^{2} M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $𝔻^{2}$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $𝔻^{2}$ -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $𝔻^{2}$ -smooth foliated diffeomorphism between two second order transverse...

On the rigidity of webs

Michel Belliart (2007)

Bulletin de la Société Mathématique de France

Similarity:

Plane $d$ -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two $d$ -webs, $d \geq 3$ are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable $d$ -webs, however, there always exists a nonmeasurable conjugacy;...

Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in $ℂ^{p}$ , for some $p > 0$ ) or differentiable (parametrized by an open neighborhood of $0$ in $ℝ^{p}$ , for some $p > 0$ ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions...

Some lagrangian invariants of symplectic manifolds

Michel Nguiffo Boyom (2007)

Banach Center Publications

Similarity:

The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by $_{F}$ (resp. $V^{F}$ ) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to $V^{F}$ . That is to say, there is a bilinear map $H^{q} (_{F}, V^{F}) \times H_{q} (_{F}, V^{F}) \to V^{F}$ , which is invariant under F-preserving symplectic...