THE NOTES ON ENERGY AND ELECTROMAGNETIC FIELD VECTORS IN THE NULL CONE Q2

Abstract

In this paper, we characterize the directional derivatives in accordance with the asymptotic orthonormal frame {x,α,y} in Q^2. Also, we express the extended Serret-Frenet relations by using cone Frenet formulas and we explain the geometrical understanding of energy on each asymptotic orthonormal vector fields in null cone. Furthermore, we express the bending elastic energy function for the same particle according to curve x(s,ξ,η) and we finalize our results by providing energy variation sketches according to directional derivatives for different cases. Additionally, we explain a geometrical interpretation of the energy for unit vector fields and we express Maxwell’s equations for the electric and magnetic field vectors in null cone 3-space.