Timelike W‐Surfaces in Minkowski 3‐Space ℝ13 and the Sinh‐Gordon Equation

Nadia Alluhaibi and Rashad A. Abdel-Baky

Journal of Applied Mathematics, 2022, vol. 2022, issue 1

Abstract: 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.

Date: 2022
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https://doi.org/10.1155/2022/7998748

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