Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations
In this work, we consider the Darboux frame T,V,U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V-direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices i...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/8624794 |
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| _version_ | 1832561539843883008 |
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| author | Nidal Echabbi Amina Ouazzani Chahdi |
| author_facet | Nidal Echabbi Amina Ouazzani Chahdi |
| author_sort | Nidal Echabbi |
| collection | DOAJ |
| description | In this work, we consider the Darboux frame T,V,U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V-direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied. |
| format | Article |
| id | doaj-art-f936dc000f194eb4a9475f0f56abefea |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f936dc000f194eb4a9475f0f56abefea2025-02-03T01:24:54ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/86247948624794Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their CharacterizationsNidal Echabbi0Amina Ouazzani Chahdi1Department of Mathematics, Ben M’Sik Faculty of Science, Hassan II Mohammedia-Casablanca University, MoroccoDepartment of Mathematics, Ben M’Sik Faculty of Science, Hassan II Mohammedia-Casablanca University, MoroccoIn this work, we consider the Darboux frame T,V,U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V-direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.http://dx.doi.org/10.1155/2021/8624794 |
| spellingShingle | Nidal Echabbi Amina Ouazzani Chahdi Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations Abstract and Applied Analysis |
| title | Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations |
| title_full | Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations |
| title_fullStr | Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations |
| title_full_unstemmed | Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations |
| title_short | Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations |
| title_sort | some special ruled surfaces generated by a direction curve according to the darboux frame and their characterizations |
| url | http://dx.doi.org/10.1155/2021/8624794 |
| work_keys_str_mv | AT nidalechabbi somespecialruledsurfacesgeneratedbyadirectioncurveaccordingtothedarbouxframeandtheircharacterizations AT aminaouazzanichahdi somespecialruledsurfacesgeneratedbyadirectioncurveaccordingtothedarbouxframeandtheircharacterizations |