On the quaternionic B2 slant helices in the semi-Euclidean space

Kahraman, Ferdağ; Gök, İsmai ̇l; ̇hoğlu, H. Hi ̇lmi ̇ Hacisali

doi:10.1016/j.amc.2011.12.007

Cited by 9 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the below relations hold: g (0) = g (0) = g (0) = g (0) = g 4 (0) = 0, g (5) = 0, (31) then the sphere contacts at fourth order to θ at θ (0). The sphere is called semi-real quaternionic osculating sphere for semi-real quaternionic curves in E 4 2 [11].…”

Section: Semi-real Quaternionic Focal Curvesmentioning

confidence: 99%

See 1 more Smart Citation

On the Quaternionic Focal Curves

Gürses¹,

Bektaș²,

Yüce³

2017

SDÜ Fen Bil Enst Der

View full text Add to dashboard Cite

In this study, a brief summary about quaternions and quaternionic curves are firstly presented. Also, the definition of focal curve is given. The focal curve of a smooth curve consists of the centers of its osculating hypersphere. By using this definition and the quaternionic osculating hyperspheres of these curves, the quaternionic focal curves in the spaces Q and Q ν with index ν = {1, 2} are discussed. Some relations about spatial semireal quaternionic curves and semi-real quaternionic curves are examined by using focal curvatures and "scalar Frenet equations" between the focal curvatures. Then, the notions: such as vertex, flattenings, a symmetry point are defined for these curves. Moreover, the relation between the Frenet apparatus of a quaternionic curve and the Frenet apparatus of its quaternionic focal curve are presented.

show abstract

Section: Semi-real Quaternionic Focal Curvesmentioning

confidence: 99%

“…After that, Frenet-Serret formulas are given by Tuna in [3] in semi-Euclidean space for quaternionic curves. By the aid of these formulae, remarkable studies of quaternionic curves are worked in literature [4,5].…”

Section: Introductionmentioning

confidence: 99%

On the Quaternionic Focal Curves

Gürses¹,

Bektaș²,

Yüce³

2017

SDÜ Fen Bil Enst Der

View full text Add to dashboard Cite

show abstract

“…In this section, we firstly mention semi-real quaternionic curve in R 4 2 . And then we characterize the semi-real quaternonic rectifying curve in R 4 2 in terms of their curvatures. As in the Section 3, the four dimensional semi-Euclidean space R 4 2 is identified with the space of unit quaternions which is denoted by Q v .…”

Section: Some Characterizations Of Semi-real Quaternionic Rectifying Curvesmentioning

confidence: 99%

“…They gave the Serret-Frenet formulas, inclined curves, harmonic curvatures and some characterizations for a quaternionic curve in the semi-Euclidean spaces E 3 1 and E 4 2 , [3]. Also, Kahraman et al's defined a new kind of slant helix in R 4 called B 2 -slant helix in R 4 2 , [4]. On the other hand, the notion of the rectifying curve is introduced in [1] as a space curve whose position vector always lies in its rectifying plane.…”

Section: Introductionmentioning

confidence: 99%

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

Eri̇şi̇r¹,

Güngör²

2014

Honam Mathematical Journal

View full text Add to dashboard Cite

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.

show abstract

“…And then SerretFrenet formulas for quaternionic curves and quaternionic inclined curves have been de…ned in Semi-Euclidean space by Çöken and Tuna [2]. Gök et al and Kahraman et al de…ned a new kind of slant helix in Euclidean space R 4 [6] and semi-Euclidean space R 4 2 [5]. It called quaternionic B 2 -slant and semi-real quaternionic B 2 -slant helix, respectively.…”

Section: Introductionmentioning

confidence: 99%