An invariant of nonpositively curved contact manifolds

Thilo Kuessner

Displaying similar documents to “An invariant of nonpositively curved contact manifolds”

Foliations with few non-compact leaves.

Vogt, Elmar (2002)

Algebraic & Geometric Topology

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Nontaut foliations and isoperimetric constants

Konrad Blachowski (2002)

Annales Polonici Mathematici

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We study nontaut codimension one foliations on closed Riemannian manifolds. We find an estimate of some constant derived from the mean curvature function of the leaves of a foliation by some isoperimetric constant of the manifold. Moreover, for foliated 2-tori and the 3-dimensional unit sphere, we find the infimum of the former constants for all nontaut codimension one foliations.

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 $r$ .

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

Elmar Vogt (1989)

Publications Mathématiques de l'IHÉS

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Foliations with all leaves compact

D. B. A. Epstein (1976)

Annales de l'institut Fourier

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The notion of the “volume" of a leaf in a foliated space is defined. If $L$ is a compact leaf, then any leaf entering a small neighbourhood of $L$ either has a very large volume, or a volume which is approximatively an integral multiple of the volume of $L$ . If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally...

The geometry of $R$ -covered foliations.

Calegari, Danny (2000)

Geometry & Topology

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Leaves of foliations with a transverse geometric structure of finite type.

Robert A. Wolak (1989)

Publicacions Matemàtiques

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In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.

De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal, James J. Hebda (1983)

Annales de l'institut Fourier

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We prove that if $M$ is a complete simply connected Riemannian manifold and $F$ is a totally geodesic foliation of $M$ with integrable normal bundle, then $M$ is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

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Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.