Curvature and Torsion Dependent Energy of Elastica and Nonelastica for a Lightlike Curve in the Minkowski Space.

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 . [ABSTRACT FROM AUTHOR]