A New Geometric Model of the Energy Functional of Lightlike Elastic Curves in Minkowski 4-Space

Abstract

In this work, we firstly describe conditions for being elastica for a moving particle corresponding to a different type of lightlike curves in Minkowski space E-1(4). Then we investigate energy on distinct lightlike elastic curves in the space and we also exploit its relationship with the energy of the same particle in the Frenet vector fields in E-1(4). Here, we use geometric descriptions of the curvature and the torsion of the curve for the computation of the energy of the lightlike elastic curves. Finally, we also characterize non-elastic lightlike curves in E-1(4) and we compute their energies to see the distinction between energies of lightlike curves of the elastic and non-elastic case in Minkowski space E-1(3).