Abstract
Let and be two timelike surfaces in Minkowski 3-space . If there exists a spacelike (timelike) Darboux line congruence between each point of and , 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.
Acknowledgments
The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, has funded this project, under Grant no. KEP-47-130-42. The authors, therefore, gratefully acknowledge the DSR technical and financial support.
Citation
Nadia Alluhaibi. Rashad A. Abdel-Baky. "Timelike -Surfaces in Minkowski 3-Space and the Sinh-Gordon Equation." J. Appl. Math. 2022 1 - 10, 2022. https://doi.org/10.1155/2022/7998748
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