Characteristic properties of the ruled surface with Darboux frame in E^3

Abstract

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

Keywords

• Ruled surface
• Darboux frame
• integral invariants.