Spinor Representations of Involute Evolute Curves in E^3
Spinor Representations of Involute Evolute Curves in E^3
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,
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- [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.
- ISSN: 2645-8845
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Fuat USTA