Comptes Rendus
no. 5
Differential geometry
A note on magnetic curves on S2n+1
[Une note sur les courbes magnétiques de S2n+1]

Présenté par : Étienne Ghys

Marian Ioan Munteanu1 ; Ana Irina Nistor2
1 University ‘Al.I. Cuza’ of Iaşi, Faculty of Mathematics, Bd. Carol I, no. 11, 700506 Iaşi, Romania
2 ‘Gheorghe Asachi’ Technical University of Iaşi, Department of Mathematics and Informatics, Bd. Carol I, no. 11, 700506 Iaşi, Romania
Comptes Rendus. Mathématique, Volume 352 (2014) no. 5, pp. 447-449.

Nous montrons qu'une courbe magnétique normale sur la sphère sasakienne S2n+1 se trouve sur une sphère totalement géodésique S3, et que la structure sasakienne sur S3 est celle qui est induite de S2n+1.

We prove that a normal magnetic curve on the Sasakian sphere S2n+1 lies on a totally geodesic sphere S3, and that the Sasakian structure on S3 is that induced from S2n+1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.03.006

Marian Ioan Munteanu 1 ; Ana Irina Nistor 2

1 University ‘Al.I. Cuza’ of Iaşi, Faculty of Mathematics, Bd. Carol I, no. 11, 700506 Iaşi, Romania
2 ‘Gheorghe Asachi’ Technical University of Iaşi, Department of Mathematics and Informatics, Bd. Carol I, no. 11, 700506 Iaşi, Romania 
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Marian Ioan Munteanu; Ana Irina Nistor. A note on magnetic curves on $ {\mathbb{S}}^{2n+1}$. Comptes Rendus. Mathématique, Volume 352 (2014) no. 5, pp. 447-449. doi : 10.1016/j.crma.2014.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.03.006/

[1] M. Barros; J.L. Cabrerizo; M. Fernández; A. Romero Magnetic vortex filament flows, J. Math. Phys., Volume 48 (2007) no. 8, p. 082904

[2] J.L. Cabrerizo; M. Fernández; J.S. Gómez The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A, Volume 42 (2009) no. 19, p. 195201

[3] J.L. Cabrerizo; M. Fernández; J.S. Gómez On the existence of almost contact structure and the contact magnetic field, Acta Math. Hungar., Volume 125 (2009) no. 1–2, pp. 191-199

[4] S.L. Druţă-Romaniuc, J. Inoguchi, M.I. Munteanu, A.I. Nistor, Magnetic curves in Sasakian and cosymplectic manifolds, preprint, 2013.

[5] M. Harada On Sasakian submanifolds, Tohoku Math. J., Volume 25 (1973) no. 2, pp. 103-109 (Collection of articles dedicated to Shigeo Sasaki on his sixtieth birthday)

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