Magnetic unit vector fields

被引：0
作者：
Jun-ichi Inoguchi
Marian Ioan Munteanu
机构：
[1] University of Tsukuba,Institute of Mathematics
[2] Hokkaido University,Department of Mathematics
[3] University Alexandru Ioan Cuza Iasi,Department of Mathematics
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2023年 / 117卷
关键词：
Dirichlet energy; Magnetic field; Harmonic map; Harmonic unit vector field; Magnetic map; Primary 53B25; Secondary 53C22; 53C43; 53D25;
D O I：
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中图分类号：
学科分类号：
摘要：
We show that a unit vector field on an oriented Riemannian manifold is a critical point of the Landau Hall functional if and only if it is a critical point of the Dirichlet energy functional. Therefore, we provide a characterization for a unit vector field to be a magnetic map into its unit tangent sphere bundle. Then, we classify all magnetic left invariant unit vector fields on 3-dimensional Lie groups.
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