Displaying similar documents to “Deforming metrics of foliations”

Differential forms, Weitzenböck formulae and foliations.

Hansklaus Rummler (1989)

Publicacions Matemàtiques

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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...

Riemannian foliations with parallel or harmonic basic forms

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

Archivum Mathematicum

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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.

De Rham decomposition theorems for foliated manifolds

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

Annales de l'institut Fourier

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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.