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

  • T. Körpinar Muş Alparslan Univ., Turkey
  • R. C. Demirkol Muş Alparslan Univ., Turkey

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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Published
18.08.2020
How to Cite
KörpinarT., and DemirkolR. C. “Curvature and Torsion Dependent Energy of Elastica and Nonelastica for a Lightlike Curve in the Minkowski Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 8, Aug. 2020, pp. 1095-0, doi:10.37863/umzh.v72i8.847.
Section
Research articles