Generated Surfaces via Inextensible Flows of Curves in R3

Abstract

We study the inextensible flows of curves in 3-dimensional Euclidean space ${\mathbb{R}}^{\mathrm{3}}$. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves in ${\mathbb{R}}^{\mathrm{3}}$. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves in ${\mathbb{R}}^{\mathrm{3}}$ and we determine the curves from their intrinsic equations (curvature and torsion). Finally, we determine and plot the surfaces that are generated by the motion of those curves by using Mathematica 7.