Riemannian manifolds not quasi-isometric to leaves in codimension one foliations

Paul A. Schweitzer

Displaying similar documents to “Riemannian manifolds not quasi-isometric to leaves in codimension one foliations”

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Similarity:

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 $Z^{k}$ ( $k \in Z_{\geq 0}$ ), then $ℱ$ is without holonomy.

A type of non-equivalent pseudogroups. Application to foliations

Jesús A. Alvarez López (1992)

Annales Polonici Mathematici

Similarity:

A topological result for non-Hausdorff spaces is proved and used to obtain a non-equivalence theorem for pseudogroups of local transformations. This theorem is applied to the holonomy pseudogroup of foliations.

An application of a theorem of Huber in holomorphic foliation theory

Hans-Jörg Reiffen (1995)

Banach Center Publications

Similarity:

Foliations with complex leaves

Giuseppe Tomassini (1995)

Banach Center Publications

Similarity:

On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki (1993)

Annales Polonici Mathematici

Similarity:

Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.

A Fatou-Julia decomposition of transversally holomorphic foliations

Taro Asuke (2010)

Annales de l’institut Fourier

Similarity:

A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when...

Foliations with Degenerate Gauss maps on $ℙ^{4}$

Thiago Fassarella (2010)

Annales de l’institut Fourier

Similarity:

We obtain a classification of codimension one holomorphic foliations on $ℙ^{4}$ with degenerate Gauss maps.

The diffeomorphism group of a Lie foliation

Gilbert Hector, Enrique Macías-Virgós, Antonio Sotelo-Armesto (2011)

Annales de l’institut Fourier

Similarity:

We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus $T^{n}$ , $n \geq 2$ . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are $\pm Id$ and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for $T^{2}$ , P. Iglesias...