On Dual Curves of DAW(k)-Type and Their Evolutes
In this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by u...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2018-09-01
|
| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1641 |
| id |
doaj-0870a1529b7a40cd852633436cede17a |
|---|---|
| record_format |
Article |
| spelling |
doaj-0870a1529b7a40cd852633436cede17a2021-08-26T13:44:39ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392018-09-01165614627329On Dual Curves of DAW(k)-Type and Their EvolutesH. S. Abdel-Aziz0M. Khalifa Saad1S. A. Mohamed2Sohag UniversityMathematics Department, Faculty of Science, Sohag UniversitySohag UniversityIn this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by using Bishop frame defined as alternatively of these curves and give some of their properties in $\mathbb{D}^{3}$. \ Moreover, we define the notion of evolutes of dual spherical curves for ruled surfaces. Finally, we give some examples to illustrate our findings.http://etamaths.com/index.php/ijaa/article/view/1641 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
H. S. Abdel-Aziz M. Khalifa Saad S. A. Mohamed |
| spellingShingle |
H. S. Abdel-Aziz M. Khalifa Saad S. A. Mohamed On Dual Curves of DAW(k)-Type and Their Evolutes International Journal of Analysis and Applications |
| author_facet |
H. S. Abdel-Aziz M. Khalifa Saad S. A. Mohamed |
| author_sort |
H. S. Abdel-Aziz |
| title |
On Dual Curves of DAW(k)-Type and Their Evolutes |
| title_short |
On Dual Curves of DAW(k)-Type and Their Evolutes |
| title_full |
On Dual Curves of DAW(k)-Type and Their Evolutes |
| title_fullStr |
On Dual Curves of DAW(k)-Type and Their Evolutes |
| title_full_unstemmed |
On Dual Curves of DAW(k)-Type and Their Evolutes |
| title_sort |
on dual curves of daw(k)-type and their evolutes |
| publisher |
Etamaths Publishing |
| series |
International Journal of Analysis and Applications |
| issn |
2291-8639 |
| publishDate |
2018-09-01 |
| description |
In this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by using Bishop frame defined as alternatively of these curves and give some of their properties in $\mathbb{D}^{3}$. \ Moreover, we define the notion of evolutes of dual spherical curves for ruled surfaces. Finally, we give some examples to illustrate our findings. |
| url |
http://etamaths.com/index.php/ijaa/article/view/1641 |
| work_keys_str_mv |
AT hsabdelaziz ondualcurvesofdawktypeandtheirevolutes AT mkhalifasaad ondualcurvesofdawktypeandtheirevolutes AT samohamed ondualcurvesofdawktypeandtheirevolutes |
| _version_ |
1721193435879178240 |