Семинар за геометрију и примене, 28. јануар 2021.

Наредни састанак Семинара биће одржан онлајн у четвртак, 28. јануара 2021 са почетком у 17:15.

Предавач: Marian Ioan Munteanu, Faculty of Mathematics, „Al.I.Cuza“,University of Iasi


Апстракт: This talk is based on some joint papers with J. Inoguchi, Institute of Mathematics, University of Tsukuba, Japan. In our paper [IM14] we define the notion of magnetic map as a generalization of both magnetic curves and harmonic maps. As a vector field can be thought of as a map from the manifold to its tangent bundle and since the tangent bundle carries a natural magnetic field obtained from its almost Kaehlerian structure, we may ask when a vector field is a magnetic map?
Furthermore, 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.

[IM14] J. Inoguchi and M.I. Munteanu, Magnetic maps, Internat. J. Geom. Methods Mod. Phys. 11 (2014) 6, art. n.1450058.
[IM15] J. Inoguchi and M.I. Munteanu, New examples of magnetic maps involving tangent bundles, Rend. Semin.Mat. Univ. Politec. Torino 73/1 (2015) 3-4, 101–116.
[IM18] J. Inoguchi and M.I. Munteanu, Magnetic vector fields: New examples, Publ. Inst. Math. Beograd 103 (117) (2018), 91-102.
[IM21] J. Inoguchi and M.I. Munteanu, Magnetic unit vector fields, submitted.

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