New geometric magnetic energy according to geometric Frenet formulas

Abstract

Geometric calculus is a special case of the Non-Newtonian Calculus introduced by Grossman and Katz (Non-Newtonian calculus, Lee Press, Pigeon Cove, 1972). Also, it is a more convenient calculation method for situations where the geometric increment is more meaningful than the arithmetic increment. In this study, geometric curves are defined and geometric Frenet-Serret formulas for these curves are presented. Furthermore, we give applications of these concepts to geometric magnetic curves.