Open AccessTimelike-Surfaces in Minkowski 3-Spaceand the Sinh-Gordon Equation
Author(s) -
Nadia Alluhaibi,
Rashad A. Abdel-Baky
Publication year - 2022
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2022/7998748
Subject(s) - minkowski space , congruence (geometry) , mathematics , geometry
Let M and M ∗ be two timelike surfaces in Minkowski 3-space ℝ 1 3 . 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.
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