CURVATURE AND TORSION DEPENDENT ENERGY OF ELASTICA AND NONELASTICA FOR A LIGHTLIKE CURVE IN THE MINKOWSKI SPACE

Abstract

We first describe the conditions for being elastica or nonelastica for a lightlike elastic Cartan curve in the Minkowski space E-1(4) by using the Bishop orthonormal vector frame and associated Bishop components. Then we compute the energy of the lightlike elastic and nonelastic Cartan curves in the Minkowski space E-1(4) and investigate its relationship with the energy of the same curves in Bishop vector fields in E-1(4). In this case, the energy functionals are computed in terms of the Bishop curvatures of the lightlike Cartan curve lying in the Minkowski space E-1(4).