A construction of hyperbolic spinors according to frenet frame in Minkowski space

Ketenci, Zeynep; Eri̇şi̇r, Tülay; Güngör, Mehmet Ali̇

doi:10.1080/1726037x.2015.1076224

Cited by 13 publications

(8 citation statements)

References 5 publications

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“…Then, considering these studies the spinor representation of the Darboux frame in E 3 was obtained by Kişi and Tosun [18]. In addition to that, the spinor representations of some curve pairs selected in Minkowski space were obtained [4,10,17]. In addition to these studies, Erişir and Karda ǧ found spinor formulations of involute-evolute curves, which are a special curve pair in Euclidean space E 3 [11] and the spinor equations of Bertrand curves were obtained in [12].…”

Section: Introductionmentioning

confidence: 99%

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

Eri̇şi̇r

İSABEYOĞLU

2023

International Electronic Journal of Geometry

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In this paper, the spinor formulations of Mannheim curve pair are investigated. First of all, two spinors matching to Mannheim curve pair are given and by considering the relationships between the Frenet frames of Mannheim curve pair, the relationship between two spinors matching to this curve pair are gotten. Therefore, a geometric interpretations of spinors are obtained using the Mannheim curve pair and considering Mannheim curve as helix the spinor formulations of Mannheim curve pair are given. Moreover, the spinor formulations are also obtained for the curvatures of the Mannheim curve pair. Consequently, an example of these spinors is obtained. Therefore, it is thought that this study will make an important contribution to the mathematical analysis and geometric interpretation of spinors, which have many uses in physics.

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Section: Introductionmentioning

confidence: 99%

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

Eri̇şi̇r

İSABEYOĞLU

2023

International Electronic Journal of Geometry

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“…Afterwards, Vivarelli obtained some relations between the spinors and quaternions, and provided the spinor representation of rotations in E 3 by utilizing the relations between the rotations in E 3 and quaternions [13,40]. In addition to these, hyperbolic spinors were studied [1,12,23,24] in Minkowski 3-space. Also, spinors have an substantial and basic role in Clifford algebra, which is called geometric algebra by W. K. Clifford, as well [5,27,28,39].…”

Section: Introductionmentioning

confidence: 99%

“…Also, spinor representation of framed Mannheim and framed Bertrand curves were investigated by Yazıcı et al [42] and ˙Işbilir et al [21], respectively. In the Minkowski-3 space, by using the concept of the hyperbolic spinors of curves in Minkowski space [23], hyperbolic spinor representations of Serret-Frenet frame [24], Darboux frame [1], and Bishop frame [12] are constructed.…”

Section: Introductionmentioning

confidence: 99%

Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space

İşbilir

Özen

Güner

2023

International Electronic Journal of Geometry

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The main goal of this study is to bring together the spinors, which have a major place in several disciplines from mathematics to physics, and Positional Adapted Frame (PAF) which is a new type frame that attracts the attention of many researchers. In accordance with this purpose, we introduce the spinor representations for the trajectories endowed with PAF in the Euclidean 3-space $\mathbb{E}^3$, and construct the spinor equations of PAF vectors. Then, we find the relations between spinor representations of PAF and Serret-Frenet frame. Also we give some results and present some geometric interpretations with respect to this relationship. Moreover, we present an illustrative numerical example in order to support the given theorems and results.

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“…In another study, spinor formulation of Bertrand curves was given [8]. Moreover, the spinor formulations of some special curves in three-dimensional Minkowski space were obtained based on these studies in three-dimensional Euclidean space [1,6,9]. In this study, a curve (α) with unit speed and a successor curve (β ) with the same arc-length parameter of the curve (α) have been considered.…”

Section: Introductionmentioning

confidence: 99%

Spinor Equations of Successor Curves

Eri̇şi̇r

ÖZTAŞ

2022

Universal Journal of Mathematics and Applications

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The aim of this study is to give spinor representation of successive curves in three-dimensional Euclidean space. In three dimensional Euclidean Space, the spinor representations of a curve with unit speed and a successor curve with the same arc length parameter as this curve has been studied. For this, first of all, the curve with unit speed and its successor curve have been corresponded to two different spinors. Then, using the relationships between these curves, the relationships between the spinors corresponding to these curves have been given. Therefore, geometric interpretations of these curves and corresponding spinors have been made. In addition, different spinor equations of the mates and derivatives of spinors have been examined and geometric interpretations of these spinor equations have been given. Then, spinor equations have been obtained in case the successive curves are helices. Consequently, two examples have been given.

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A construction of hyperbolic spinors according to frenet frame in Minkowski space

Cited by 13 publications

References 5 publications

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space

Spinor Equations of Successor Curves

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