Ruled Surfaces according to Rotation Minimizing Frame

TL;DR

This paper studies ruled surfaces generated by straight lines using the rotation minimizing frame, providing conditions for developability and new results on special curves on these surfaces.

Contribution

It introduces new conditions for developability of ruled surfaces via RMF and explores properties of asymptotic, geodesic, and curvature lines.

Findings

Derived necessary and sufficient conditions for developability.

Established new theorems on asymptotic, geodesic, and curvature lines.

Enhanced understanding of ruled surfaces using rotation minimizing frames.

Abstract

In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is developable. Also, we give some new results and theorems related to be the asymptotic curve, the geodesic curve and the line of curvature of the base curve on the ruled surface.