Smarandache Curves of Mannheim Curve Couple According to Frenet Frame

Abstract

In this paper, when the Frenet vectors of the partner curve of Mannheim curve are taken as the position vectors, the curvature and the torsion of Smarandache curves are calculated. These values are expressed depending upon the Mannheim curve. Besides, we illustrate example of our main results.

NC -Smarandache Ruled Surface and NW -Smarandache Ruled Surface according to Alternative Moving Frame in E

“…Definition 4 (see [15]). NW-Smarandache curves according to the alternative frame of the curve c � c(s) are given by…”

“…Generally, a Smarandache curve defines a curve whose position vector is composed by a moving frame vectors on another regular curve. In [15], one can find two Smarandache curves introduced according to the alternative moving frame. It concerns NC−Smarandache curves and NW−Smarandache curves.…”

A New Approach For Smarandache Curves

“…They used the known relation between the Darboux and Frenet frame to research special Smarandache curves of timelike curve which is on timelike surface. Additionally the studies of this type of curve can be found out in literature [8,12,[15][16][17].…”

Smarandache Curves According to Sabban Frame of the anti-Salkowski Indicatrix Curve

“…Smarandache curves in Euclidean 3-space are defined and some features of these curves are given in [9]. For some authors worked on the Smarandache curve also may be seen in [10,11]. In 1990, the geodesic curve of a spherical curve is calculated by J. Koenderink with the Sabban frame of the spherical indicatrix curves in [12].…”