Ruled Surfaces With the Bishop Frame in Euclidean 3-Space

In this study, we examined the ruled surfaces in Euclidean 3-space with the Bishop frame of the base curve in two cases and obtained some characterizations on the ruled surfaces by using its directrix, Bishop curvatures, shape operator and Gauss curvature. Furthermore, we calculated Bishop Steiner rotation, Bishop tranlation vectors, the pitch and angle of pitch of the ruled surfaces and gave some sufficient and necessary conditions for developable ruled surface with respect to the Bishop frame of the base curve by using Bishop curvatures and curvatures of the ruled surface along the generating lines.