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Timelike W-Surfaces in Minkowski 3-Space R^3_1 and the Sinh-Gordon Equation

Rashad A. Abdel-Baky, M. T. Aldossary

Abstract


Let M and M* are two timelike surfaces in Minkowski 3-Space R^3_1. 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.

Keywords


Darboux Line congruence, Weingarten surfaces, Backlund’s transformation.

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