CONTRIBUTION TO NULL KILLING MAGNETIC TRAJECTORIES
International Journal of Maps in Mathematics, vol.3, no.2, pp.129-138, 2020 (Scopus)
- Publication Type: Article / Article
- Volume: 3 Issue: 2
- Publication Date: 2020
- Journal Name: International Journal of Maps in Mathematics
- Journal Indexes: Scopus
- Page Numbers: pp.129-138
- Keywords: Geodesic curvature, Lorentz force equation, Null magnetic curve, Timelike surface
- Isparta University of Applied Sciences Affiliated: Yes
Abstract
We analyze null magnetic trajectories of a magnetic field on a timelike surface in Minkowski 3−space (formula presented). We show that the Lorentz force can be written into the Darboux frame field of a null trajectory on the surface. We give the necessary and sufficient condition for writing a null curve as the magnetic trajectory of the magnetic field. After creating a variation, we derive the Killing magnetic flow equations with regard to the geodesic curva-ture, geodesic torsion and normal curvature of the curve γ on the timelike surface. Finally we examine the geodesics of some timelike surfaces in (formula presented).