Le but de ce travail est de démontrer quelques propriétés de l’ensemble-limite , au sens de Reeb, des bouts des feuilles des feuilletages de codimension 1, lorsque tend vers d’un seul côté, puis lorsque est un feuilletage de classe .
We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of -models. We also apply our method to rigidity problems of some group actions.
This paper concerns projectively Anosov flows with smooth stable and unstable foliations and on a Seifert manifold . We show that if the foliation or contains a compact leaf, then the flow is decomposed into a finite union of models which are defined on and bounded by compact leaves, and therefore the manifold is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible...
In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.
Every open manifold of dimension greater than one has complete Riemannian metrics with bounded geometry such that is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...
We introduce topological 𝒬-holonomy groupoids for singular foliations (M,ℱ) with an Ehresmann connection 𝒬 using 𝒬-holonomy groups, which have a global character. We show advantage of our groupoids over known ones.
Compact, -foliated manifolds of codimension one, having all leaves proper, are shown to be -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class and of class for every nonnegative integer .