Notes on magnetic curves in 3D semi-Riemannian manifolds

Authors : Zehra ÖZDEMİR, İsmail GÖK, Yusuf YAYLI, Faik Nejat EKMEKCİ

Pages : 412-426

Doi:10.3906/mat-1408-31

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :A magnetic field is defined by the property that its divergence is zero in three-dimensional semi-Riemannian manifolds. Each magnetic field generates a magnetic flow whose trajectories are curves $\gamma $, called magnetic curves. In this paper, we investigate the effect of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on three-dimensional semi-Riemannian manifolds. We then investigate the trajectories of these magnetic fields and give some characterizations and examples of these curves.
Keywords : Special curves, vector fields, flows, ordinary differential equations