Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $
The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ \mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-06-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231047?viewType=HTML |
| _version_ | 1797784191383896064 |
|---|---|
| author | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_facet | Areej A. Almoneef Rashad A. Abdel-Baky |
| author_sort | Areej A. Almoneef |
| collection | DOAJ |
| description | The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ \mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples. |
| first_indexed | 2024-03-13T00:36:27Z |
| format | Article |
| id | doaj.art-0e93ee807a5c4c8489de908487ebc891 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T00:36:27Z |
| publishDate | 2023-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0e93ee807a5c4c8489de908487ebc8912023-07-10T01:20:10ZengAIMS PressAIMS Mathematics2473-69882023-06-0189205462056010.3934/math.20231047Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $Areej A. Almoneef 0Rashad A. Abdel-Baky11. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia2. Department of Mathematics, Faculty of Science, University of Assiut 71516, EgyptThe main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ \mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.https://www.aimspress.com/article/doi/10.3934/math.20231047?viewType=HTMLgeodesic curvebertrand materuled surface |
| spellingShingle | Areej A. Almoneef Rashad A. Abdel-Baky Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ AIMS Mathematics geodesic curve bertrand mate ruled surface |
| title | Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ |
| title_full | Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ |
| title_fullStr | Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ |
| title_full_unstemmed | Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ |
| title_short | Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $ |
| title_sort | surface family pair with bertrand pair as mutual geodesic curves in euclidean 3 space mathbb e 3 |
| topic | geodesic curve bertrand mate ruled surface |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231047?viewType=HTML |
| work_keys_str_mv | AT areejaalmoneef surfacefamilypairwithbertrandpairasmutualgeodesiccurvesineuclidean3spacemathbbe3 AT rashadaabdelbaky surfacefamilypairwithbertrandpairasmutualgeodesiccurvesineuclidean3spacemathbbe3 |