On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$

Abstract

In this paper, it has been researched curves lying on parallel-like surfaces $M^{f}$ of the ruled surface $M$ in $E^{3}$. Using the definition of parallel-like surfaces it has been found parametric expressions of parallel-like surface of the ruled surface and image curve of the directrix curve of the base surface. Moreover, obtaining Darboux frames of curves lying on surfaces $M$ and $M^{f}$, it has been compared the geodesic curvatures, the normal curvatures and the geodesic torsions of these curves.