Generated Surfaces via Inextensible Flows of Curves inR3

Abstract

We study the inextensible flows of curves in 3-dimensional Euclidean spaceR3. The main purpose of this paper is constructing and plotting the surfaces that are generated from the motion of inextensible curves inR3. Also, we study some geometric properties of those surfaces. We give some examples about the inextensible flows of curves inR3and 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.

On Surfaces Constructed by Evolution According to Quasi Frame

“…An evolving curve can be thought as a collection of curves parameterized by time. This means that each curve in the collection has a space parameter s and a time parameter t, [3]. The following definitions can be given according to quasi frame in R 3 considering references [6] and [7].…”

Timelike Surfaces of Evolution in Minkowski 3-Space

“…An evolving curve can be thought as a collection of curves parameterized by time. This means that each curve in the collection has a space parameter and a time parameter , [2]. For example, Korpinar [3] investigated the surfaces constructed by the binormal spherical indicatrix of a space curve.…”

“…Selçuk University, Graduate School of Natural Sciences, Konya, Turkey. E-mail: y.yavuz42@yahoo.com.tr 2. Selçuk University, Department of Mathematics, Konya, Turkey.…”

Second Binormal Motions of Inextensible Curves in 4-dimensional Galilean Space

“…Inextensible curve and surface flows also arise in the context of many problems in computer vision [6], [12] and computer animation [9], and even structural mechanics [17]. Papers in [5], [11], [13], [14] and [18] are obtained some new characterizations of the inextensible curve flows curves. By drawing inspiration from them, in this paper, we consider the second binormal motions of inextensible curves in Galilean 4-space.…”