Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
type: Item
instance of: scholarly article
title: Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
zbMATH Open document ID: 1035.53089
DOI: 10.1016/S0926-2245(02)00060-8
published in: Differential Geometry and its Applications
publication date: 2002-08-14T00:00:00Z
review text: A unit vector field \(X\) on a closed Riemannian manifold \(M\) can be viewed as a map of \(M\) into the unit tangent bundle \(T^1 M\). Since the metric on \(M\) induces a metric on \(T^1 M\), one can look for such vector fields which minimise the energy. The authors show that under some additional curvature condition, unit Killing vector fields on closed 3-manifolds have this property. This leads to examples on quotients of unimodular 3-dimensional Lie groups.
Mathematics Subject Classification ID: 53C43
zbMATH DE Number: 1780872
zbMATH Keywords: Killing vector fields
zbMATH Keywords: harmonic sections of the unit tangent bundle
zbMATH Keywords: energy minimizers
Wikidata QID: Q115338221
author: J. C. González-Dávila
author: Lieven Vanhecke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1780872