Displaying similar documents to “Connexions associated with foliated structures”

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...

Special connections on smooth 3-web manifolds

Vanžurová, Alena

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For a three-web W of codimension n on a differentiable manifold M 2 n of dimension 2 n , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.

The automorphism groups of foliations with transverse linear connection

Nina Zhukova, Anna Dolgonosova (2013)

Open Mathematics

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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...

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.

Connections for non-holonomic 3-webs

Vanžurová, Alena

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A non-holonomic 3-web is defined by two operators P and B such that P is a projector, B is involutory, and they are connected via the relation P B + B P = B . The so-called parallelizing connection with respect to which the 3-web distributions are parallel is defined. Some simple properties of such connections are found.

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.