engleski

On Killing magnetic curves in hyperboloid model of SL(2,R) geometry

Magnetic curves represent trajectories of charged particles moving on a Riemannian manifold under the action of a magnetic field. A vector field X is a Killing vector field if the Lie derivative with respect to X of the ambient space metric g vanishes. The Killing vector field can be interpreted as an infinitesimal generator of isometry on the manifold in the sense that the flow generated by this field is a continuous isometry of the manifold. The trajectories corresponding to the Killing magnetic fields are called the Killing magnetic curves. We consider the Killing magnetic curves in hyperboloid model of SL(2, R) space.

Magnetic curve ; Killing vector field ; SL(2, R) geometry

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