On the characterisations of ruled surface pairs according to the Sabban frame

Abstract

In this study, we introduce ruled surface pairs according to the Sabban frame of the curve defined on a unit sphere. First, the conditions of each couple of two ruled surface pairs to be simultaneously developable and minimal are investigated. Then, the asymptotic, geodesic and line of curvature of the parameter curves of the ruled surface pairs are simultaneously characterized. Also, we examined whether the direction curves and the stiction curves of the ruled surface pairs coincide. Finally, the examples of the ruled surface pairs are given, and their graphs are drawn.