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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021200?viewType=HTML |
| _version_ | 1818722780788555776 |
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| author | Rashad Abdel-Baky Mohamed Khalifa Saad |
| author_facet | Rashad Abdel-Baky Mohamed Khalifa Saad |
| author_sort | Rashad Abdel-Baky |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T21:00:04Z |
| format | Article |
| id | doaj.art-164a8dc14e6a42c4a60483e0d44e5228 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-17T21:00:04Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-164a8dc14e6a42c4a60483e0d44e52282022-12-21T21:32:45ZengAIMS PressAIMS Mathematics2473-69882021-01-01643339335110.3934/math.2021200Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $Rashad Abdel-Baky0Mohamed Khalifa Saad 11. Mathematics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt2. Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt 3. Mathematics Department, Faculty of Science, Islamic University of Madinah, Al-Madinah, KSAIn 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.http://www.aimspress.com/article/doi/10.3934/math.2021200?viewType=HTMLe. study mapserret–frenet formulaerectifying dual curvedual helices |
| spellingShingle | Rashad Abdel-Baky Mohamed Khalifa Saad Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ AIMS Mathematics e. study map serret–frenet formulae rectifying dual curve dual helices |
| title | Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ |
| title_full | Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ |
| title_fullStr | Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ |
| title_full_unstemmed | Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ |
| title_short | Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $ |
| title_sort | some characterizations of dual curves in dual 3 space mathbb d 3 |
| topic | e. study map serret–frenet formulae rectifying dual curve dual helices |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021200?viewType=HTML |
| work_keys_str_mv | AT rashadabdelbaky somecharacterizationsofdualcurvesindual3spacemathbbd3 AT mohamedkhalifasaad somecharacterizationsofdualcurvesindual3spacemathbbd3 |