On electromagnetic curves and geometric phase associated with frontals in de-Sitter 2-space

Abstract

In this work, we introduce a Berry phase model which is very important in physics relative to the frontals in de-Sitter 2-space. With this approach, we examine the relationship between a singular curve and Fermi-Walker's law and Berry's phase law in de-Sitter 2-space. We give the Rytov curves by using an orthonormal frame of spacelike frontals and timelike frontals with Fermi-Walker parallelism. We express parametric representations of Rytov curves associated with a singular optical fiber. We examine electromagnetic curves associated with orthonormal vectors of spacelike frontals and timelike frontals in de-Sitter 2-space. Hence, we express the magnetic field equations, Lorentz force equations and magnetic trajectory equations along a singular optical fiber. Finally, we give examples that support the theories both physically and geometrically.