Spinor Representations of Involute Evolute Curves in E^3

Tülay Erişir; Neslihan Cansu Kardağ

doi:10.33401/fujma.562536

Research Article

Year 2019, Volume: 2 Issue: 2, 148 - 155, 20.12.2019

Tülay Erişir Neslihan Cansu Kardağ

https://doi.org/10.33401/fujma.562536

Cited By: 8

Abstract

References

[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 R31 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.

Spinor Representations of Involute Evolute Curves in E^3

Year 2019, Volume: 2 Issue: 2, 148 - 155, 20.12.2019

Tülay Erişir Neslihan Cansu Kardağ

https://doi.org/10.33401/fujma.562536

Cited By: 8

Abstract

In this paper, we have obtained spinor with two complex components representations of Involute Evolute curves in $\mathbb{E}^3$. Firstly, we have given the spinor equations of Frenet vectors of two curves which are parameterized by arc-length and have 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 $\mathbb{E}^3$?". Finally, we have given an example which crosscheck to theorems throughout this study.

Keywords

Involute Evolute Curves, Spinors

References

[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 R31 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.

There are 15 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Tülay Erişir 0000-0001-6444-1460 Neslihan Cansu Kardağ This is me 0000-0001-6444-1460
Publication Date	December 20, 2019
Submission Date	May 9, 2019
Acceptance Date	November 12, 2019
Published in Issue	Year 2019 Volume: 2 Issue: 2

Cite

APA	Erişir, T., & Kardağ, N. C. (2019). Spinor Representations of Involute Evolute Curves in E^3. Fundamental Journal of Mathematics and Applications, 2(2), 148-155. https://doi.org/10.33401/fujma.562536
AMA	Erişir T, Kardağ NC. Spinor Representations of Involute Evolute Curves in E^3. FUJMA. December 2019;2(2):148-155. doi:10.33401/fujma.562536
Chicago	Erişir, Tülay, and Neslihan Cansu Kardağ. “Spinor Representations of Involute Evolute Curves in E^3”. Fundamental Journal of Mathematics and Applications 2, no. 2 (December 2019): 148-55. https://doi.org/10.33401/fujma.562536.
EndNote	Erişir T, Kardağ NC (December 1, 2019) Spinor Representations of Involute Evolute Curves in E^3. Fundamental Journal of Mathematics and Applications 2 2 148–155.
IEEE	T. Erişir and N. C. Kardağ, “Spinor Representations of Involute Evolute Curves in E^3”, FUJMA, vol. 2, no. 2, pp. 148–155, 2019, doi: 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 2/2 (December 2019), 148-155. https://doi.org/10.33401/fujma.562536.
JAMA	Erişir T, Kardağ NC. Spinor Representations of Involute Evolute Curves in E^3. FUJMA. 2019;2:148–155.
MLA	Erişir, Tülay and Neslihan Cansu Kardağ. “Spinor Representations of Involute Evolute Curves in E^3”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 2, 2019, pp. 148-55, doi:10.33401/fujma.562536.
Vancouver	Erişir T, Kardağ NC. Spinor Representations of Involute Evolute Curves in E^3. FUJMA. 2019;2(2):148-55.