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HYPERBOLIC SPINOR DARBOUX EQUATIONS OF SPACELIKE CURVES IN MINKOWSKI 3-SPACE
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 Title & Authors
HYPERBOLIC SPINOR DARBOUX EQUATIONS OF SPACELIKE CURVES IN MINKOWSKI 3-SPACE
Balci, Yakup; Erisir, Tulay; Gungor, Mehmet Ali;
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 Abstract
In this paper, we study on spinors with two hyperbolic components. Firstly, we express the hyperbolic spinor representation of a spacelike curve dened on an oriented (spacelike or time-like) surface in Minkowski space . Then, we obtain the relation between the hyperbolic spinor representation of the Frenet frame of the spacelike curve on oriented surface and Darboux frame of the surface on the same points. Finally, we give one example about these hyperbolic spinors.
 Keywords
hyperbolic space;hyperbolic spinors;Frenet formula;
 Language
English
 Cited by
 References
1.
F. Antonuccio, Hyperbolic Numbers and the Dirac Spinor, arXiv:hepth/9812036v1, 1998.

2.
M. Carmeli, Group Theory and General Relativity, Representations of the Lorentz Group and Their Applications to the Gravitational Field. McGraw-Hill, New York, Imperial College Press, 1977.

3.
E. Cartan, The theory of spinors. Dover, New York, 1981.

4.
G. F. T. Del Castillo, Spinors in Four-Dimensional Spaces, Springer New York Dordrecht Heidelberg London, 2009.

5.
G. F. T. Del Castillo, G. S. Barrales, Spinor formulation of the di erential geometry of curves. Revista Colombiana de Matematicas 38 (2004), 27-34.

6.
P. A. M. Dirac, Spinors in Hilbert Space. Plenum Press, 1974.

7.
P. A. M. Dirac, The quantum theory of the electron, Proceedings of the Royal Society of London A117: JSTOR 94981, (1928), 610-624. crossref(new window)

8.
M. P. Do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ, 1976.

9.
T. Erisir, M. A. Gungor, and M. Tosun, Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame, Adv. in Appl. Clifford Algebr. 25 (2015), no. 4, 799-810. crossref(new window)

10.
T. Ikawa, On curves and submanifolds in an indefinite-Riemannian manifold. Tsukuba J. Math. 9 (1985), no. 2, 353-371. crossref(new window)

11.
Z. Ketenci, T. Erisir, and M. A. Gungor, Spinor Equations of Curves in Minkowski Space, V. Congress of the Turkic World Mathematicians, Kyrgyzstan, June 05-07, 2014.

12.
I. Kisi and M. Tosun, Spinor Darboux Equations of Curves in Euclidean 3-Space. Math. Morav. 19 (2015), no. 1, 87-93. crossref(new window)

13.
P. Kustaanheimo and E. Stiefel, Perturbation Theory of Kepler Motion Based on Spinor Regularization, J. Reine Angew. Math. 218 (1965), 204-219.

14.
B. W. Montague, Elemenatry spinor algebra for polarized beams in strage rings, Particle Accelerators 11 (1981), 219-231.

15.
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.

16.
M. Ozdemir and A. A. Ergin, Spacelike Darboux curves in Minkowski 3-space. Differ. Geom. Dyn. Syst. 9 (2007), 131-137.

17.
W. Pauli, Zur Quantenmechanik des magnetischen Elektrons, Zeitschrift fr Physik 43 (9-10) (1927), 601-632. crossref(new window)

18.
D. H. Sattinger and O. L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics. Springer-Verlag, New York, 1986.

19.
S. I. Tomonaga, The Quantity Which Is Neither Vector nor Tensor, The story of spin, University of Chicago Press, p. 129, ISBN 0-226-80794-0, 1998.

20.
D. Unal, I. Kisi and M. Tosun, Spinor Bishop Equation of Curves in Euclidean 3-Space. Adv. in Appl. Clifford Algebr. 23 (2013), no. 3, 757-765. crossref(new window)

21.
I. M. Yaglom, A Simple non-Euclidean Geometry and its Physical Basis. Springer-Verlag, New-York, 1979.