On characteristic curves of developable surfaces in Euclidean 3-space

TL;DR

This paper explores the relationship between characteristic curves on developable surfaces in Euclidean 3-space, identifying specific types of base curves when parameter curves coincide with these characteristic curves.

Contribution

It characterizes the base curves of developable surfaces as plane curves, circular helices, general helices, or slant helices under certain conditions.

Findings

Base curves can be plane, circular helix, general helix, or slant helix.

Parameter curves coinciding with characteristic curves lead to specific base curve types.

Provides geometric classification of developable surfaces based on characteristic curves.

Abstract

We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix, a general helix or a slant helix.