Some special types of developable ruled surface

Abstract

In this study we consider the focal curve C $gamma$ of a space curve $gamma$ and its focal curvatures. We characterize some special types of ruled surface, choosing one of the base curves or director curves as the focal curve of the space curve $gamma$ . Finally we construct new types of ruled surface and calculate their distinguished parameters. We give necessary and sufficient conditions for these types of ruled surface to become developable.