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arXiv · 2107.05423

Magnetic unit vector fields

Jun-ichi Inoguchi·Marian Ioan Munteanu
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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 $3$-dimensional Lie groups.

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Jun-ichi Inoguchi, Marian Ioan Munteanu. 2021-07-12. Magnetic unit vector fields. https://doi.org/10.1007/s13398-023-01399-6

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