On evolute curves in terms of inextensible flows of in E³

Talat Körpınar

doi:10.5269/bspm.v36i1.31619

Abstract

In this paper, we study inextensible flows of evolute curve of curves in E³. We research inextensible flows evolute curves of in the E³.

Highlights

The variable s is employed to denote arc length along a space curve
For ∀s ∈ I, the curve β is called the evolute of the curve r, if the tangent at the point β(s) to the curve β passes through the tangent at the point r(s) to the curve β and
= f T + gN + hB be a smooth flow of the curve r in

Summary

Introduction

The variable s is employed to denote arc length along a space curve. Note that the arc-length parameterization r : s → r(s) of a curve satisfies r′(s) = 1 and r′(s) ⊥ r′′(s) for all s. B(s) = T(s) × N(s) are, respectively, the unit tangent, principal normal, and binormal vectors of the curve at the point r(s).

Results

Conclusion