Characteristic properties of the ruled surface with Darboux frame in E3

Abstract

In this study, the ruled surface with Darboux frame is defined. Then, the ruled surfaces characteristic properties which are related to the geodesic curvature, the normal curvature and the geodesic torsion are investigated. The relation between the Darboux frame and the Frenet frame on the ruled surface is presented. Moreover, some theorems about the pitch and the angle of the pitch which are the integral invariants of the ruled surface with darboux frame are given.