Notes on magnetic curves in 3D semi-Riemannian manifolds

Authors

ZEHRA ÖZDEMİR
İSMAİL GÖK
YUSUF YAYLI
FAİK NEJAT EKMEKCİ

DOI

10.3906/mat-1408-31

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

First Page

412

Last Page

426

Recommended Citation

ÖZDEMİR, ZEHRA; GÖK, İSMAİL; YAYLI, YUSUF; and EKMEKCİ, FAİK NEJAT (2015) "Notes on magnetic curves in 3D semi-Riemannian manifolds," Turkish Journal of Mathematics: Vol. 39: No. 3, Article 10. https://doi.org/10.3906/mat-1408-31
Available at: https://journals.tubitak.gov.tr/math/vol39/iss3/10