On the characterization of the particular magnetic curves in De-Siter 2-space

In the first section, fundamental theorems and definitions related to the differential geometry of curves, magnetic curves, and the De-Sitter 2-spacetime structure are presented. The second section provides an introduction that emphasizes the manuscript's importance and includes a literature review based on previous works. The third section characterizes timelike tangent magnetic curves and their associated magnetic vector fields, timelike normal magnetic curves and their associated magnetic vector fields, and timelike magnetic curves and their associated magnetic vector fields, defined in De-Sitter 2-spacetime. The fourth section introduces a fundamental law of Newton that highlights the effects of frictional force, normal force, and gravitational force on a given particle. It describes three novel types of timelike magnetic curves, respectively called timelike frictional magnetic curves, timelike normal force magnetic curves, and timelike gravitational magnetic curves together with their associated magnetic vector fields in De-Sitter 2-space. The geometric characterization and physical modeling of these curves are obtained by considering the well-known formula of the Lorentz force combined with Newton's formula. In the fifth section, the gyroradius, angular and mechanical momentum, potential energy, and torque of the charged particle corresponding to each magnetic curve defined in the previous section are calculated. The final section demonstrates the practical applicability of our findings and highlights the potential for future research in the field of physical modeling using magnetic curves and differential geometry.