Spinor Representations of Involute Evolute Curves in $E^3$

KARDAĞ, Neslihan Cansu; Erişir, Tülay

doi:10.33401/fujma.562536

Spinor Representations of Involute Evolute Curves in $E^3$

Tülay ERİŞİR, (Erzincan Binali Yıldırım Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Erzincan, Türkiye)

Neslihan Cansu KARDAĞ (Erzincan Binali Yıldırım Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Erzincan, Türkiye)

Fundamental journal of mathematics and applications (Online)

1 0

Yıl: 2019 Cilt: 2 Sayı: 2 Sayfa Aralığı: 148 - 155 Metin Dili: İngilizce DOI: 10.33401/fujma.562536 İndeks Tarihi: 04-09-2020

Spinor Representations of Involute Evolute Curves in $E^3$

Öz:

In this paper, we have obtained spinor with two complex components representations ofInvolute Evolute curves in $E^3$. Firstly, we have given the spinor equations of Frenet vectorsof 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 matchedthese curves with different spinors. Then, we have investigated the answer of question”How are the relationships between the spinors corresponding to the Involute Evolute curvesin $E^3$?”. Finally, we have given an example which crosscheck to theorems throughout thisstudy

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] E. Cartan, ´ The Theory of Spinors, The M.I.T. Press, Cambridge, MA, 1966.
[2] H. B. Lawson, M. L. Michelsohn, Spin Geometry, Princeton University Press, New Jersey, 1989.
[3] P. O’Donnell, Introduction to 2-Spinors in General Relativity, World Scientific Publishing Co. Pte. Ltd., London, 2003.
[4] M. D. Vivarelli, Development of spinors descriptions of rotational mechanics from Euler’s rigid body displacement theorem, Celestial Mech., 32 (1984), 193–207.
[5] G. F. T. Del Castillo, G. S. Barrales, Spinor formulation of the differential geometry of curves, Rev. Colombiana Mat., 38 (2004), 27–34.
[6] I. Kis¸i, M. Tosun, Spinor Darboux equations of curves in Euclidean 3-space, Math. Morav., 19(1) (2015), 87–93.
[7] D. Unal, I. Kisi, M. Tosun, Spinor Bishop equation of curves in Euclidean 3-space, Adv. Appl. Clifford Algebr., 23(3) (2013), 757–765.
[8] Z. Ketenci, T. Erisir, M.A. Gungor, A construction of hyperbolic spinors according to Frenet frame in Minkowski space, J. Dyn. Syst. Geom., Theor. 13(2) (2015), 179–193.
[9] T. Erisir, M. A. Gungor, M. Tosun. Geometry of the hyperbolic spinors corresponding to alternative frame, Adv. Appl. Clifford Algebr., 25(4) (2015), 799–810.
[10] Y. Balci, T. Erisir, M. A. Gungor, Hyperbolic spinor Darboux equations of spacelike curves in Minkowski 3-space, J. Chungcheong Math. Soc., 28(4) (2015), 525–535.
[11] M. Tarakcioglu, T. Erisir, M. A. Gungor, M. Tosun. The hyperbolic spinor representation of transformations in R 3 1 by means of split quaternions, Adv. Appl. Clifford Algebr., 28(1) (2018), 26.
[12] H. H. Hacisalihoglu, Differential Geometry, Faculty of Science, Ankara University, 1, 1996.
[13] H. Goldstein, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, Mass., 1980.
[14] D. H. Sattinger, O. L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, Springer-Verlag, New York, 1986.
[15] W. T. Payne, Elementary spinor theory, Amer. J. Phys., 20 1952, 253.

APA	Erişir T, KARDAĞ N (2019). Spinor Representations of Involute Evolute Curves in $E^3$. , 148 - 155. 10.33401/fujma.562536
Chicago	Erişir Tülay,KARDAĞ Neslihan Cansu Spinor Representations of Involute Evolute Curves in $E^3$. (2019): 148 - 155. 10.33401/fujma.562536
MLA	Erişir Tülay,KARDAĞ Neslihan Cansu Spinor Representations of Involute Evolute Curves in $E^3$. , 2019, ss.148 - 155. 10.33401/fujma.562536
AMA	Erişir T,KARDAĞ N Spinor Representations of Involute Evolute Curves in $E^3$. . 2019; 148 - 155. 10.33401/fujma.562536
Vancouver	Erişir T,KARDAĞ N Spinor Representations of Involute Evolute Curves in $E^3$. . 2019; 148 - 155. 10.33401/fujma.562536
IEEE	Erişir T,KARDAĞ N "Spinor Representations of Involute Evolute Curves in $E^3$." , ss.148 - 155, 2019. 10.33401/fujma.562536
ISNAD	Erişir, Tülay - KARDAĞ, Neslihan Cansu. "Spinor Representations of Involute Evolute Curves in $E^3$". (2019), 148-155. https://doi.org/10.33401/fujma.562536

APA	Erişir T, KARDAĞ N (2019). Spinor Representations of Involute Evolute Curves in $E^3$. Fundamental journal of mathematics and applications (Online), 2(2), 148 - 155. 10.33401/fujma.562536
Chicago	Erişir Tülay,KARDAĞ Neslihan Cansu Spinor Representations of Involute Evolute Curves in $E^3$. Fundamental journal of mathematics and applications (Online) 2, no.2 (2019): 148 - 155. 10.33401/fujma.562536
MLA	Erişir Tülay,KARDAĞ Neslihan Cansu Spinor Representations of Involute Evolute Curves in $E^3$. Fundamental journal of mathematics and applications (Online), vol.2, no.2, 2019, ss.148 - 155. 10.33401/fujma.562536
AMA	Erişir T,KARDAĞ N Spinor Representations of Involute Evolute Curves in $E^3$. Fundamental journal of mathematics and applications (Online). 2019; 2(2): 148 - 155. 10.33401/fujma.562536
Vancouver	Erişir T,KARDAĞ N Spinor Representations of Involute Evolute Curves in $E^3$. Fundamental journal of mathematics and applications (Online). 2019; 2(2): 148 - 155. 10.33401/fujma.562536
IEEE	Erişir T,KARDAĞ N "Spinor Representations of Involute Evolute Curves in $E^3$." Fundamental journal of mathematics and applications (Online), 2, ss.148 - 155, 2019. 10.33401/fujma.562536
ISNAD	Erişir, Tülay - KARDAĞ, Neslihan Cansu. "Spinor Representations of Involute Evolute Curves in $E^3$". Fundamental journal of mathematics and applications (Online) 2/2 (2019), 148-155. https://doi.org/10.33401/fujma.562536