Displaying similar documents to “Harmonic conformal flows on manifolds of constant curvature”

Deforming metrics of foliations

Vladimir Rovenski, Robert Wolak (2013)

Open Mathematics

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Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the...

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.