On Rectifying Dual Space Curves

Abstract

We give some characterizations of the rectifying curves in the dual space and show that rectifying dual space curves can be stated with the aid of dual unit spherical curves. Thus, we have a link between rectifying dual space curves and classical surfaces in the Euclidean three-space.

Normal and Spherical Curves in Dual Space D 3

“…where T is unit tangent vector of the indicatrix ( ) t α which is a real space curve in 3 E [7,9]. From the last equality we can write Since T is unit, from the differentiation of T with respect to dual arc length parameter s we have…”

“…The characterizations of rectifying and normal curves in Euclidean space and Minkowski space have been given some authors [1,4,5,6]. The corresponding characterizations of the rectifying dual curves in dual space have been given by Yücesan, Ayyıldız and Çöken [9]. Furthermore, Önder has defined and studied dual timelike normal and dual timelike spherical curves in dual Minkowski space 3…”

“…dual torsion of α . Similar to the Euclidean case, the planes spanned by { } called the dual osculating plane, the dual rectifying plane and the dual normal plane, respectively[9].3. Dual Normal Curves in3 D In this section, we give definition and characterizations of normal curves in dual space 3 in dual space 3 D .…”

Some Special Curves in Dual 3-Space

“…So the set of oriented lines in Euclidean space E 3 is one to one correspondence with the points of dual space in D 3 . Recently, dual space curves and surfaces have been extensively studied and they are powerful mathematical tools for spherical motion in D 3 [1,4,9,10].…”

A Study on Rectifying Curves in the Dual Lorentzian Space

“…In [6], the authors have characterized non-null and null rectifying curves lying fully in the Minkowski 3-space. Yücesan, Ayyıldız, and Çöken have given some characterizations of the rectifying curves in the dual space D 3 [11].…”