Magnetic maps
type: Item
instance of: scholarly article
title: Magnetic maps
zbMATH Open document ID: 1317.53024
DOI: 10.1142/S0219887814500583
author: Jun-ichi Inoguchi
author: Marian Ioan Munteanu
published in: International Journal of Geometric Methods in Modern Physics
publication date: 2014-10-29T00:00:00Z
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 6362162
zbMATH Keywords: magnetic curves
zbMATH Keywords: action integral
zbMATH Keywords: Landau Hall functional
zbMATH Keywords: harmonic maps
zbMATH Keywords: contact magnetic fields
MaRDI profile type: Publication
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full work available at URL: s0219887814500583
OpenAlex ID: W4236743754
review text: The authors introduce magnetic maps as critical points of the Landau-Hall integral and characterize them in terms of prescribed tension fields. Let \((N, h)\) and \((M, g)\) be two Riemannian manifolds and let \(f: (N, h)\longrightarrow (M, g)\) be a smooth map. Let \(\xi\) be a global vector field on \(N\) and \(\omega\) be a 1-form on \(M\). Then they prove that \(f\) is a magnetic map with respect to \(\xi\) and \(\omega\) if and only if it satisfies NEWLINE\[NEWLINE \tau(f) = \phi(f_{*}\xi), NEWLINE\]NEWLINE where \(\tau(f)\) is the tension field of \(f\) and \(\omega\) is defined by \(g(\phi X, Y)= d\omega(X, Y)\), for all \(X\), \(Y\) tangent on \(M\). They provide some examples in Euclidean, contact and Kähler manifolds, and study some classes of magnetic surfaces in Euclidean 3-spaces.
reviewed by: Fortuné Massamba
description: scientific article; zbMATH DE number 6362162