Article
The contact magnetic flow in 3D Sasakian manifolds
Author/s | Cabrerizo Jaraíz, José Luis
Fernández Andrés, Manuel Gómez Casanueva, Juan Salvador |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2009-05-15 |
Deposit Date | 2016-10-19 |
Published in |
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Abstract | We first present a geometrical approach to magnetic fields in three-dimensional Riemannian manifolds, because this particular dimension allows one to easily tie vector fields and 2-forms. When the vector field is divergence ... We first present a geometrical approach to magnetic fields in three-dimensional Riemannian manifolds, because this particular dimension allows one to easily tie vector fields and 2-forms. When the vector field is divergence free, it defines a magnetic field on the manifold whose Lorentz force equation presents a simple and useful form. In particular, for any three-dimensional Sasakian manifold the contact magnetic field is studied, and the normal magnetics trajectories are determined. As an application, we consider the three-dimensional unit sphere, where we prove the existence of closed magnetic trajectories of the contact magnetic field, and that this magnetic flow is quantized in the set of rational numbers. |
Funding agencies | Junta de Andalucía |
Project ID. | MTM 2007-61284
FQM-327 |
Citation | Cabrerizo Jaraíz, J.L., Fernández Andrés, M. y Gómez Casanueva, J.S. (2009). The contact magnetic flow in 3D Sasakian manifolds. Journal of Physics A: Mathematical and Theoretical, 42 (19), 195201-195210. |
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