Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $
In this work, we prove that the ratio of torsion and curvature of any dual rectifying curve is a non-constant linear function of its dual arc length parameter. Thereafter, a dual differential equation of third order is constructed for every dual curve. Then, several well-known characterizations of d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021200?viewType=HTML |
| Summary: | In this work, we prove that the ratio of torsion and curvature of any dual rectifying curve is a non-constant linear function of its dual arc length parameter. Thereafter, a dual differential equation of third order is constructed for every dual curve. Then, several well-known characterizations of dual spherical, normal and rectifying curves are consequences of this differential equation. Finally, we prove a simple new characterization of dual spherical curves in terms of the Darboux vector. |
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| ISSN: | 2473-6988 |