A geometric approach on the energy of a lightlike curve in minkowski space E-1(4)

Abstract

In this paper, we firstly give characterization of a moving particle whose trajectories correspond to different type of lightlike curves in Minkowski space E-1(4). We firstly present kinematical framework of lightlike curves in Minkowski space E-1(4). Then we compute energy on the particle corresponding to different type of lightlike curves defined in Minkowski space E-1(4). Furthermore, we assume that each lightlike curve has a bending feature of elastica. Thus, we determine a connection between energy of lightlike curves in Frenet vector fields and bending energy functional of elastica.