Classification of Killing magnetic curves in ℍ3
Abstract
In this paper, we study classification of magnetic curves corresponding to Killing vector fields of ℍ3. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional (α)-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.
- Publication:
-
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- December 2023
- DOI:
- 10.1142/S0219887824500063
- arXiv:
- arXiv:2309.03859
- Bibcode:
- 2023IJGMM..2050006K
- Keywords:
-
- Almost contact manifolds;
- killing magnetic curves;
- hyperbolic spaces;
- Mathematical Physics;
- 53D15;
- 53C80;
- 57K32
- E-Print:
- 33 pages, to appear in International Journal of Geometric Methods in Modern Physics