Flow equations of some associated curves

This study consists of four main parts. In the first section, an introduction to our work is given. The mathematical and physical issues included in our study are introduced and relevant studies in the literature are mentioned. In the second chapter, definitions and theorems regarding principal direction curves, adjoint curves, flow equations and energy of the vector field are given. In the third section, the flow equations of the adjoint curves are given; vortex filament, Belavin-Polyakov and Landau-Lifshitz flow equations were discussed as subheadings. The energy equations of the vector fields representing these flow equations were obtained. In the fourth chapter, the flow equations of the principal direction curves are given; Vortex filament, Belavin-Polyakov and Landau-Lifshitz flow equations were discussed as subheadings. The energy equations of the vector fields representing these flow equations were obtained.