Hyperbolic Spinor Darboux Equations of Spacelike Curves in Minkowski 3-Space

Balci, Y.; Eri̇şi̇r, Tülay; Güngör, Mehmet Ali̇

doi:10.14403/jcms.2015.28.4.525

Cited by 17 publications

(12 citation statements)

References 6 publications

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“…al obtained the spinor representation of the Bishop frame, an alternative frame, of a curve in the three-dimensional Minkowski space, and the spinor formulation of the relationship between Frenet frame and Bishop frame, [9]. Also, the Darboux frame on the oriented surface in E 3 1 was obtained by the aid of hyperbolic spinors, [10]. Moreover, in [11] Tarakçıoǧlu et.…”

Section: Introductionmentioning

confidence: 99%

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Spinor Representations of Involute Evolute Curves in E^3

Eri̇şi̇r

Kardağ

2019

Fundamental Journal of Mathematics and Applications

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In this paper, we have obtained spinor with two complex components representations of Involute Evolute curves in E 3. Firstly, we have given the spinor equations of Frenet vectors of two curves which are parameterized by arc-length and have an arbitrary parameter. Moreover, we have chosen that these curves are Involute Evolute curves and have matched these curves with different spinors. Then, we have investigated the answer of question "How are the relationships between the spinors corresponding to the Involute Evolute curves in E 3 ?". Finally, we have given an example which crosscheck to theorems throughout this study.

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Section: Introductionmentioning

confidence: 99%

“…Frenet frame and Bishop frame, [9]. Also, the Darboux frame on the oriented surface in E 3 1 was obtained by the aid of hyperbolic spinors, [10]. Moreover, in [11] Tarakçıoǧlu et.…”

Section: Introductionmentioning

confidence: 99%

Spinor Representations of Involute Evolute Curves in E^3

Eri̇şi̇r

Kardağ

2019

Fundamental Journal of Mathematics and Applications

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“…Erişir, M. Ali Güngör and M. Tosun iii. Spin(4) = SU (2) × SU (2), and the half-spin representations are the fundamental representations on the two copies of SU (2). iv.…”

Section: Introductionmentioning

confidence: 99%

“…iv. Spin (5) = Sp (2), and the spin representation on C 4 can be identified with the fundamental Sp (2) representation on H 2 . v. Spin (6) = SU (4), and each of the half-spin representations on C 4 can be identified with the fundamental SU (4) representation on C 4 [18].…”

Section: Introductionmentioning

confidence: 99%

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Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame

Eri̇şi̇r

Güngör

Tosun

2015

Adv. Appl. Clifford Algebras

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In this paper, we study to express the theory of curves including a wide section of Lorentzian geometry in terms of spinors with two hyperbolic components which has an important place in the Clifford algebra. In other words, we express the rotation, element of SO(1, 3), between the Frenet frame and the other frame defined as alternatively of the (spacelike or timelike) curves in Minkowski space R 3 1 in terms of the rotation, element of SU (2, H), with the aid of the hyperbolic spinors.Mathematics Subject Classification. 62J05, 62J07.

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