Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space
Based on the E. Study's map, we study a timelike ruled surface as a curve on the hyperbolic dual unit sphere in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$. Then, as applications of the singularity theory of smooth functions, we define the notation of evolutes for timelike ruled surfaces and e...
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| Language: | English |
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Etamaths Publishing
2017-11-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1534 |
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doaj-c74b90effee24f198a1f748397aea72e2021-08-26T13:44:38ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392017-11-01152114124269Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-SpaceRashad A. Abdel-Baky0Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, EGYPTBased on the E. Study's map, we study a timelike ruled surface as a curve on the hyperbolic dual unit sphere in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$. Then, as applications of the singularity theory of smooth functions, we define the notation of evolutes for timelike ruled surfaces and establish the relationships between their geometric invariants. Finally, an example of application is introduced and explained in detail.http://etamaths.com/index.php/ijaa/article/view/1534 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rashad A. Abdel-Baky |
| spellingShingle |
Rashad A. Abdel-Baky Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space International Journal of Analysis and Applications |
| author_facet |
Rashad A. Abdel-Baky |
| author_sort |
Rashad A. Abdel-Baky |
| title |
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space |
| title_short |
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space |
| title_full |
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space |
| title_fullStr |
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space |
| title_full_unstemmed |
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space |
| title_sort |
evolutes of hyperbolic dual spherical curve in dual lorentzian 3-space |
| publisher |
Etamaths Publishing |
| series |
International Journal of Analysis and Applications |
| issn |
2291-8639 |
| publishDate |
2017-11-01 |
| description |
Based on the E. Study's map, we study a timelike ruled surface as a curve on the hyperbolic dual unit sphere in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$. Then, as applications of the singularity theory of smooth functions, we define the notation of evolutes for timelike ruled surfaces and establish the relationships between their geometric invariants. Finally, an example of application is introduced and explained in detail. |
| url |
http://etamaths.com/index.php/ijaa/article/view/1534 |
| work_keys_str_mv |
AT rashadaabdelbaky evolutesofhyperbolicdualsphericalcurveinduallorentzian3space |
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1721193529267453952 |