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The contact magnetic flow in 3D Sasakian manifolds

 

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Author: Cabrerizo Jaraíz, José Luis
Fernández Andrés, Manuel
Gómez Casanueva, Juan Salvador
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2009-05-15
Published in: Journal of Physics A: Mathematical and Theoretical, 42 (19), 195201-195210.
Document type: Article
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 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.
Cite: 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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URI: http://hdl.handle.net/11441/47724

DOI: 10.1088/1751-8113/42/19/195201

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