Deforming metrics of foliations

Vladimir Rovenski; Robert Wolak

Displaying similar documents to “Deforming metrics of foliations”

Harmonic conformal flows on manifolds of constant curvature

Amine Fawaz (2007)

Open Mathematics

Similarity:

We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.

Mean curvature functions for codimension-one foliations with all leaves compact

Paweł Grzegorz Walczak (1984)

Czechoslovak Mathematical Journal

Similarity:

Differential forms, Weitzenböck formulae and foliations.

Hansklaus Rummler (1989)

Publicacions Matemàtiques

Similarity:

The Weitzenböck formulae express the Laplacian of a differential form on an oriented Riemannian manifold in local coordinates, using the covariant derivatives of the form and the coefficients of the curvature tensor. In the first part, we shall describe a certain "differential algebra formalism" which seems to be a more natural frame for those formulae than the usual calculations in local coordinates. In this formalism there appear some interesting differential operators...

A characterization of harmonic foliations by the volumepreserving property of the normal geodesic flow.

Kim, Hobum (2002)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Riemannian foliations with parallel or harmonic basic forms

Fida El Chami, Georges Habib, Roger Nakad (2015)

Archivum Mathematicum

Similarity:

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.

Foliations by minimal surfaces and contact structures on certain closed 3-manifolds.

Escobales, Richard H.jun. (2003)

International Journal of Mathematics and Mathematical Sciences

Similarity:

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.

Riemannian foliations on Manifolds with non-negative curvature.

Philippe Tondeur, Hobum Kim (1992)

Manuscripta mathematica

Similarity:

Nontaut foliations and isoperimetric constants

Konrad Blachowski (2002)

Annales Polonici Mathematici

Similarity:

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.