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

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Ukrainian Mathematical Journal Aims and scope

We first describe the conditions for being elastica or nonelastica for a lightlike elastic Cartan curve in the Minkowski space \( {\mathbbm{E}}_1^4 \) 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 \( {\mathbbm{E}}_1^4 \) and investigate its relationship with the energy of the same curves in Bishop vector fields in \( {\mathbbm{E}}_1^4 \). In this case, the energy functionals are computed in terms of the Bishop curvatures of the lightlike Cartan curve lying in the Minkowski space \( {\mathbbm{E}}_1^4 \).

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Authors and Affiliations

  1. Muş Alparslan University, Muş, Turkey

    T. Körpinar & R. C. Demirkol

Authors
  1. T. Körpinar
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  2. R. C. Demirkol
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Correspondence to R. C. Demirkol.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 8, pp. 1095–1105, August, 2020. Ukrainian DOI: 10.37863/umzh.v72i8.847.

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Körpinar, T., Demirkol, R.C. Curvature and Torsion Dependent Energy of Elastica and Nonelastica for a Lightlike Curve in the Minkowski Space. Ukr Math J 72, 1267–1279 (2021). https://doi.org/10.1007/s11253-020-01853-3

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  • DOI: https://doi.org/10.1007/s11253-020-01853-3

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