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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Bibliographic Details
Published inJournal of applied mathematics Vol. 2022
Main Authors Alluhaibi, Nadia, Abdel-Baky, Rashad A.
Format Journal Article
LanguageEnglish
Published New York Hindawi 01.01.2022
Hindawi Limited
Wiley
Subjects
Euclidean space
Minkowski space
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2022/7998748