Narrow Results

The aim of this paper is to obtain magnetic trajectories corresponding to contact magnetic fields in Lorentzian $\alpha$-Sasakian 3-manifolds. First, we provide the definitions of the magnetic field and the Lorentzian equation used in this paper and derive the expression for the Bott connection by using the Levi-Civita connection. Then we derive the expression of Killing vector fields by using the Killing equation. At the same time, we obtain the explicit formulas for the Killing magnetic curves related to Bott connection. In addition, we provide an example for each type of Killing magnetic curve.

In this paper, we define the notion of Bott connection in the Heisenberg group $({ℍ}_3,g)$ and derive the expression of the Bott connection by using the Levi-Civita connection. Moreover, we derive the expressions of killing vector fields by using the killing equation and obtain some explicit formulas for killing magnetic curves associated to the Bott connection. Furthermore, we give some examples of killing magnetic curves.