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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Research Article

Geometrical Aspects of Motion of Charged Particles in Magnetic and Killing Magnetic Fields and Their Corresponding Trajectories in Anti-De Sitter 3-Space

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pp. 191–226Vol. 20Issue 2July 2022DOI: 10.1080/1726037X.2022.2142355XML
Received:
02 Apr 2022
Accepted:
04 Jul 2022
Published Online:
13 Nov 2022
Article type:
Research Article
Language:
EN
Article no.:
1726037X.2022.2142355
Pages:
191–226

Abstract

We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space . Primarily, we characterize magnetic trajectories in in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for (where corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on which constitutes a basis for the corresponding 6D Lie algebra i(). We conclude with characterizations of Killing magnetic trajectories in with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).

Keywords

Anti-de Sitter 3-spaceFrenet apparatusMagnetic fieldLorentz forceMagnetic trajectorySplit-quaternionKilling vector field

Subject Classifications

53C2253C4053C5053Z0578A35

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