Displaying similar documents to “Translation foliations of codimension one on compact affine manifolds”

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

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Let ℱ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of ℱ is isomorphic to Z , then ℱ is without holonomy. We also show that if π 2 ( M ) ≅ 0 and the fundamental group of each leaf of ℱ is isomorphic to Z k ( k ∈ Z ≥ 0 ), then ℱ is without holonomy.

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.

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.

Lagrangian holonomy ; characteristic elements of a lagrangian foliation

Carlos Currás-Bosch, Pierre Molino (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let ℒ be a lagrangian foliation on a symplectic manifold ( M 2 n , ω ) . The characteristic elements of such a foliation associated to a lagrangian total transversal are obtained; they are a generalisation of the characteristic elements given by J.J. Duistermaat [5]. This technique is applied to give a classification of the germs of lagrangian foliation along a compact leaf. Several examples of classification are given.