Ruled Surfaces with Bishop vectors via Smarandache geometry

The paper studies new ruled surfaces with the vectors of Bishop frame via Smarandache geometry. The fundamental forms and the corresponding curvatures are provided for each ruled surface to draw characteristics of the surfaces such as developability and minimality. Moreover, the properties of the base curve and the corresponding striction curves of each surface are also discussed through asymptoticity, geodesicity and principal line. It is found that a ruled surface designed by Bishop vectors of a slant helix-like curve apart from other special kinds of curves has a direct effect on the characteristics of some constructed ruled surfaces.