Magnetic unit vector fields
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Publication:6372581
DOI10.1007/S13398-023-01399-6zbMATH Open1517.53063arXiv2107.05423MaRDI QIDQ6372581
Jun-ichi Inoguchi, Marian Ioan Munteanu
Publication date: 12 July 2021
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.
Analysis on real and complex Lie groups (22E30) Differential geometric aspects of harmonic maps (53C43) Natural bundles (58A32)
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