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. The first, the conditions for 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 characterised. In addition, we examined whether the direction curves and the striction curves of the ruled surface pairs coincide. Finally, examples of the ruled surface pairs are given, and their graphs are drawn. © 2025, University of Nis. All rights reserved.