Notes on magnetic curves in 3D semi-Riemannian manifolds
TURKISH JOURNAL OF MATHEMATICS, vol.39, no.3, pp.412-426, 2015 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 39 Issue: 3
- Publication Date: 2015
- Doi Number: 10.3906/mat-1408-31
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.412-426
- Keywords: Special curves, vector fields, flows, ordinary differential equations, HELICES
- Ankara University Affiliated: Yes
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.