Curvature and torsion dependent energy of elastica and nonelastica for a lightlike curve in the Minkowski space
Abstract
UDC 515.1
We firstly describe conditions for being elastica or nonelastica for a lightlike elastic Cartan curve in the Minkowski space $\mathbb{E}_{1}^{4}$ by using the Bishop orthonormal vector frame and associated Bishop components. Then we compute the energy of the lightlike elastic and nonelastic Cartan curve in the Minkowski space $\mathbb{E}_{1}^{4}$ and investigate its relationship with the energy of the same curve in Bishop vector fields in $\mathbb{E}_{1}^{4}$. Here, energy functionals are computed in terms of Bishop curvatures of the lightlike Cartan curve lying in the Minkowski space $\mathbb{E}_{1}^{4}$.
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