A New Version Darboux Vector and Characterization Some Special Curves According to Type-2 Bishop Frame in $$\mathbb {R}^{3}$$ R 3
| Autor: | Süha Yilmaz, Umit Ziya Savcı |
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| Rok vydání: | 2017 |
| Předmět: |
Physics::Biological Physics
Quantitative Biology::Biomolecules Mathematical analysis General Physics and Astronomy Type (model theory) Characterization (mathematics) Omega Darboux vector Combinatorics Nonlinear Sciences::Exactly Solvable and Integrable Systems Euclidean geometry Helix Constant (mathematics) Arc length Mathematics |
| Zdroj: | Proceedings of the National Academy of Sciences, India Section A: Physical Sciences. 87:355-362 |
| ISSN: | 2250-1762 0369-8203 |
| DOI: | 10.1007/s40010-017-0373-6 |
| Popis: | In this paper, we introduce a new Darboux vector and Darboux helix a curve according to type-2 Bishop frame in $$ \mathbb {R}^{3}$$ . We defined a new Darboux vector in term of type-2 Bishop frame in $$ \mathbb {R}^{3}$$ . We introduce a new spherical indicatrix, Darboux helix and constant precession of the curve type-2 Bishop in Euclidean 3-space. We give new characterization between Darboux helix and general helix. Apart from, the following characterization is given. The curve $$\alpha \in $$ $$ \mathbb {R} ^{3}$$ is an inclined curve if and only if the arc length $$s_{\omega _{0}}$$ of the Darboux spherical indicatrix of the $$\alpha $$ is constant. Finally we illustrate one example of our main results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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