The graph of a totally geodesic foliation

Robert A. Wolak

Displaying similar documents to “The graph of a totally geodesic foliation”

De Rham decomposition theorems for foliated manifolds

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

Annales de l'institut Fourier

Similarity:

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.

The automorphism groups of foliations with transverse linear connection

Nina Zhukova, Anna Dolgonosova (2013)

Open Mathematics

Similarity:

The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian...

Foliations admitting transverse systems of differential equations

Robert Wolak (1988)

Compositio Mathematica

Similarity:

Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

Similarity:

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.

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.

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.

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

Robert A. Wolak (1989)

Publicacions Matemàtiques

Similarity:

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.

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

Paul A. Schweitzer (2011)

Annales de l’institut Fourier

Similarity:

Every open manifold $L$ of dimension greater than one has complete Riemannian metrics $g$ with bounded geometry such that $(L, g)$ is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of $(L, g)$ suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of $(L, g)$ that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry....