On the quaternionic Smarandache curves in Euclidean 3-space

Abstract

In this paper, we give the definitions of quaternionic Smarandache curves in 3-dimensional Euclidean space 3 E and we investigate some differential geometric properties of these curves.

On Spatial Quaternionic Involute Curve A New View

“…A regular curve Minkowski space, whose position vector is composed by Frenet vectors on another regular curve, is called Smarandache curve [13]. Special Smarandache curves have been studied by some authors [1,3,10,12,13]. Let γ = γ(s) spatial quaternionic curve and {t, n 1 , n 2 } be its moving FrenetSerret frame.…”

“…They have given the definitions of quaternionic Smarandache curves in E 3 and investigated some *Corresponding author. differential geometric properties of these curves [3]. After general definition of quaternions, relations between real quaternions and Serret-Frenet formulas have been investigated.…”

A Note on Special Smarandache Curves in the Null Cone Q

“…The popularity of Smarandache curves in various ambient spaces have been classfied in [1]- [7], [13]- [16]. In this study, we define special Smarandache curves such as xαβ, xβy, xαy, αβy-Smarandache curves according to asymptotic orthonormal frame in the null cone Q 3 and we examine the curvatures and the asymptotic orthonormal frame's vectors of Smarandache curves.…”

Surfaces family with common Smarandache asymptotic curve

“…Special Smarandache curves such as -Smarandache curves according to Sabban frame in Euclidean unit sphere has introduced in [9]. Also, they give some characterization of Smarandache curves and illustrate examples of their results.On the Quaternionic Smarandache Curves in Euclidean 3-Space have been investigated in [10].…”