Seminar za geometriju i primene, 28. januar 2021.

Naredni sastanak Seminara biće održan onlajn u četvrtak, 28. januara 2021 sa početkom u 17:15.

Predavač: Marian Ioan Munteanu, Faculty of Mathematics, "Al.I.Cuza", University of Iasi

Naslov predavanja: VECTOR FIELDS AND MAGNETIC MAPS

Apstrakt:
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.

References:
[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.

Meeting link:
https://matf.webex.com/matf/j.php?MTID=mb567d186f7c1ef9495dafcc3e2b148af
Meeting number (access code): 174 382 3473
Meeting password: 9bqY7rAv26C.


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