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

Year 2023, Volume: 72 Issue: 4, 867 - 879, 29.12.2023

Semra Yurttançıkmaz

https://doi.org/10.31801/cfsuasmas.1187854

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.

Keywords

Ruled surface, parallel-like surface, Darboux frame

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