Ruled surfaces obtained by bending of curves

Uğur GÖZÜTOK,Hüsnü Anıl ÇOBAN,Yasemin SAĞIROĞLU

doi:10.3906/mat-1908-21

Abstract

We consider a first-order infinitesimal bending of a curve in R3 to obtain a ruled surface. This paper investigates this kind of ruled surfaces and their properties. Also, we obtain conditions for ruled surfaces obtained by bending to be developable.

Highlights

The history of differential geometry dates back to the beginning of the 19th century
The ruled surfaces with vanishing Gaussian curvature, which can be transformed into the plane without any deformation and distortion, are called developable surfaces
The ruled surface obtained by bending of r is a map r : I × (−ε, ε) −→ R3 defined by r(u, v) = r(u) + vz(u), where z(u) is the infinitesimal bending field of the curve r and u ∈ I, v ∈ (−ε, +ε) for ε → 0

Summary

Introduction

The history of differential geometry dates back to the beginning of the 19th century. We consider the infinitesimal bending of a curve to obtain a ruled surface.

Results

Conclusion