CONTRIBUTION TO NULL KILLING MAGNETIC TRAJECTORIES

ÖZKAN TÜKEL G., TURHAN T.

International Journal of Maps in Mathematics, vol.3, no.2, pp.129-138, 2020 (Scopus) identifier

  • 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).