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In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator.  We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface.  Moreover, the  parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

STUDYING ON A SKEW RULED SURFACE BY USING THE GEODESIC FRENET TRIHEDRON OF ITS GENERATOR