Surface Families With Common Mannheim-B Curvature Line

Abstract

In this study, we obtain necessary and sufficient conditions for the Mannheim B curve pair of the curve given by the Bishop frame in to be both parametric and curvature lines on the surface given by its parametric equation. Then, the same situation was expressed in the case of a ruled surface, which is a special and important type of surface, and the conditions for developable it among these surfaces were examined. Finally, examples supporting the study were given through the Maple15 program.