Magnetic trajectories in three-dimensional Lie groups

TURHAN T.

Mathematical Methods in the Applied Sciences, vol.43, no.5, pp.2747-2758, 2020 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.1002/mma.6081
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2747-2758
  • Keywords: Lie groups, Lorentz force equation, magnetic flow, magnetic trajectory
  • Isparta University of Applied Sciences Affiliated: No

Abstract

We study magnetic trajectories in Lie groups equipped with bi-invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi-invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G.