Curvature and torsion dependent energy of elastica and nonelastica for a lightlike curve in the Minkowski space
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 ligh...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/847 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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| DOI: | 10.37863/umzh.v72i8.847 |