Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation
Let M and M∗ be two timelike surfaces in Minkowski 3-space ℝ13. If there exists a spacelike (timelike) Darboux line congruence between each point of M and M∗, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and th...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7998748 |
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| author | Nadia Alluhaibi Rashad A. Abdel-Baky |
| author_facet | Nadia Alluhaibi Rashad A. Abdel-Baky |
| author_sort | Nadia Alluhaibi |
| collection | DOAJ |
| description | Let M and M∗ be two timelike surfaces in Minkowski 3-space ℝ13. If there exists a spacelike (timelike) Darboux line congruence between each point of M and M∗, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found. |
| format | Article |
| id | doaj-art-b0842181690144969c81b6ce1a321aaa |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b0842181690144969c81b6ce1a321aaa2025-02-03T01:12:13ZengWileyJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/7998748Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon EquationNadia Alluhaibi0Rashad A. Abdel-Baky1Department of MathematicsDepartment of MathematicsLet M and M∗ be two timelike surfaces in Minkowski 3-space ℝ13. If there exists a spacelike (timelike) Darboux line congruence between each point of M and M∗, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund’s transformation. Finally, a method to construct new timelike Weingarten surface has been found.http://dx.doi.org/10.1155/2022/7998748 |
| spellingShingle | Nadia Alluhaibi Rashad A. Abdel-Baky Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation Journal of Applied Mathematics |
| title | Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation |
| title_full | Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation |
| title_fullStr | Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation |
| title_full_unstemmed | Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation |
| title_short | Timelike W-Surfaces in Minkowski 3-Space ℝ13 and the Sinh-Gordon Equation |
| title_sort | timelike w surfaces in minkowski 3 space r13 and the sinh gordon equation |
| url | http://dx.doi.org/10.1155/2022/7998748 |
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