Abstract: Izumiya and Takeuchi (2003) obtained some characterizations for Ruled surfaces. Turgut and Hacısalihoğlu (1998) defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi (1995) and Jung and Pak (1996) studied Ruled surfaces. This study uses the method in (Izumiya and Takeuchi, 2003) to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R₁³. We have studied singularities of the rectifying developable (surface) of a timelike curve. We observed that the rectifying developable along a timelike curve α is non-singular if and only if α is a cylindrical helice. In this case the rectifying developable is a cylindrical surface.

Key words: Timelike Ruled surfaces, Bertrand curve, Cylindrical helices

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