Curvature and torsion dependent energy of elastica and nonelastica for a lightlike curve in the Minkowski space

UDC 515.1We firstly describe conditions for being elastica or nonelastica for a lightlike elastic Cartan curve in the Minkowski space by using the Bishop orthonormal vector frame and associated Bishop components.  Then we compute the energy of the lightlike elastic and nonelastic Cartan curve in the Minkowski space and investigate its relationship with the energy of the same curve in Bishop vector fields in .  Here, energy functionals are computed in terms of Bishop curvatures of the lightlike Cartan curve lying in the Minkowski space .