Magnetic unit vector fields
Differential Geometry
2023-02-24 v2
Abstract
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 -dimensional Lie groups.
Keywords
Cite
@article{arxiv.2107.05423,
title = {Magnetic unit vector fields},
author = {Jun-ichi Inoguchi and Marian Ioan Munteanu},
journal= {arXiv preprint arXiv:2107.05423},
year = {2023}
}
Comments
25 pages