Harmonicity and minimality of oriented distributions
type: Item
instance of: scholarly article
title: Harmonicity and minimality of oriented distributions
zbMATH Open document ID: 1073.58007
DOI: 10.1007/BF02803502
author: J. C. González-Dávila
author: O. Gil-Medrano
author: Lieven Vanhecke
published in: Israel Journal of Mathematics
publication date: 2005-03-07T00:00:00Z
review text: Let \(M\) be a Riemannian manifold. The total space \(P\) of the Grassmann bundle of oriented \(k\)-dimensional vector subspaces of \(TM\) naturally inherits a Riemannian metric. The authors consider sections in the Grassmann bundle, i.e. oriented distributions, as maps between the Riemannian manifolds \(M\) and \(P\) and derive conditions under which such a distribution yields a harmonic map or a minimal immersion. They show that the \(3\)-dimensional distribution of \(S^{4m+3}\) tangent to the quternionic Hopf fibration defines a harmonic map and a minimal immersion. These results are extended to more general situations docming from \(3\)-Sasaki and quaternionic geometry.
reviewed by: Christian Bär
Mathematics Subject Classification ID: 58A30
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 2141377
zbMATH Keywords: distribution
zbMATH Keywords: harmonic map
zbMATH Keywords: minimal immersion
zbMATH Keywords: Hopf fibration
zbMATH Keywords: Grassmann bundle
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02803502
OpenAlex ID: W1976438170
description: scientific article; zbMATH DE number 2141377