Magnetic curves on surfaces in lorentzian 3-space

In this thesis, we will determine magnetic trajectories on surfaces in Lorentzian 3-space. For this, we will first introduce the magnetic vector field and magnetic curves in Lorentzian 3-space. Then we will obtain the Killing equations of Darboux frame curvatures on the surfaces. We will determine the magnetic curves on the surfaces in Lorentzian 3 space by making a variational approach with the help of Kiling equations. In practice, we will determine the magnetic curves on the time-like Lorentz sphere, called de Sitter space, and on the space-like Lorentz sphere, called the hyperbolic plane. In addition, we will give examples suitable for the results obtained and visualize these examples with the help of computer programs.