SOME CHARACTERIZATIONS OF QUATERNIONIC RECTIFYING CURVES IN THE SEMI-EUCLIDEAN SPACE 𝔼₂⁴

Abstract

The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and n2 of the curve, [1]. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifying curves in R 3 1 . Moreover, by the aid of these characterizations, we have investigated semi real quaternionic rectifying curves in semiquaternionic space Qv.

Pseudo Quaterniyonik Lorentzian Evolute and İnvolute Eğriler İçin Yeni Bir Yaklaşım

“…First, the geometric properties of transformations using quaternionic and pseudo-quaternionic multiplications in 4-dimensional real vector space are given by Baharatti and Nagaraj, [3]. Later, some results were expressed by studying quaternionic curves in different spaces (eg Euclidean and Lorentzian spaces) by many mathematicians, [4,8,12]. As mentioned above, although the quaternionic curve and quaternionic Lorentzian curve has been studied by many mathematicians, this article is a different study with the quaternion terminology for a quaternionic Lorentzian curve.…”

“…Bükcü and Karacan studied on the evolute and involute curves on Lorentzian space [7]. Soyfidan and Güngör also have studied this issue [8]. Kalkan et al have studied on this issue for some special curves [9].…”

On Spatial Quaternionic Involute Curve A New View

“…Erişir and Güngör have obtained some characterizations of semi-real spatial quaternionic rectifying curves in IR 1 3 . Moreover, by the aid of these characterizations, they have investigated semi real quaternionic rectifying curves in semi-quaternionic space [6]. Şenyurt and Ç alkan found the Darboux vector of the spatial quaternionic curve according to the Frenet frame.…”

An application according to spatial quaternionic Smarandache curve

“…Following, quaternionic inclined curves have been defined and harmonic curvatures studied by Karadag and Sivridag, [7]. In, Tuna and Çöken have studied quaternion valued functions and quaternionic inclined curves in the semi-Euclidean space E 4 2 , [9]. They have given the Serret-Frenet formulae for the quaternionic curve in the semi-Euclidean space.Then they have defined quaternionic inclined curves and harmonic curvatures for the quaternionic curves in the semi-Euclidean space.…”

“…He has studied Frenet-Serret invariants of a special case. In [4], Erişir and Güngör have obtained some characterizations of semi-real spatial quaternionic rectifying curves in IR 3 1 . Moreover, by the aid of these characterizations, they have investigated semi real quaternionic rectifying curves in semi quaternionic space.…”