Sweeping Surfaces in theThree-Dimensional Lie Group
This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obta...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/698 |
| _version_ | 1797409295171584000 |
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| author | Sahar H. Nazra Rashad A. Abdel-Baky |
| author_facet | Sahar H. Nazra Rashad A. Abdel-Baky |
| author_sort | Sahar H. Nazra |
| collection | DOAJ |
| description | This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obtained. In particular, we mostly focused on the study of the resulting developable surface is a cylinder, cone, or tangent surface. Meanwhile, to support the results in the paper, some illustrative examples are presented. |
| first_indexed | 2024-03-09T04:11:10Z |
| format | Article |
| id | doaj.art-eef38144571e466cba67ce4e87b265b2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:11:10Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-eef38144571e466cba67ce4e87b265b22023-12-03T14:00:01ZengMDPI AGSymmetry2073-89942022-03-0114469810.3390/sym14040698Sweeping Surfaces in theThree-Dimensional Lie GroupSahar H. Nazra0Rashad A. Abdel-Baky1Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 24382, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, EgyptThis paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obtained. In particular, we mostly focused on the study of the resulting developable surface is a cylinder, cone, or tangent surface. Meanwhile, to support the results in the paper, some illustrative examples are presented.https://www.mdpi.com/2073-8994/14/4/698Lie groupssweeping surfacelocal singularities |
| spellingShingle | Sahar H. Nazra Rashad A. Abdel-Baky Sweeping Surfaces in theThree-Dimensional Lie Group Symmetry Lie groups sweeping surface local singularities |
| title | Sweeping Surfaces in theThree-Dimensional Lie Group |
| title_full | Sweeping Surfaces in theThree-Dimensional Lie Group |
| title_fullStr | Sweeping Surfaces in theThree-Dimensional Lie Group |
| title_full_unstemmed | Sweeping Surfaces in theThree-Dimensional Lie Group |
| title_short | Sweeping Surfaces in theThree-Dimensional Lie Group |
| title_sort | sweeping surfaces in thethree dimensional lie group |
| topic | Lie groups sweeping surface local singularities |
| url | https://www.mdpi.com/2073-8994/14/4/698 |
| work_keys_str_mv | AT saharhnazra sweepingsurfacesinthethreedimensionalliegroup AT rashadaabdelbaky sweepingsurfacesinthethreedimensionalliegroup |