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A construction of hyperbolic spinors according to frenet frame in Minkowski space
*Zeynep KetenciCorresponding authorzeynepketenci@ogr.sakarya.edu.trSAKARYA UNIVERSITY, FACULTY OF ARTS AND SCIENCE, DEPARTMENT OF MATHEMATICSSAKARYA/TURKEYView full profile → , Tülay ErişirSAKARYA UNIVERSITY, FACULTY OF ARTS AND SCIENCE, DEPARTMENT OF MATHEMATICSSAKARYA/TURKEYView full profile → , Mehmet Ali GüngörSAKARYA UNIVERSITY, FACULTY OF ARTS AND SCIENCE, DEPARTMENT OF MATHEMATICSSAKARYA/TURKEYView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 16 Feb 2015
- Accepted:
- 06 Jun 2015
- Published Online:
- 03 Jul 2015
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2015.1076224
- Pages:
- 179–193
Abstract
In this paper, spinors which consists of two hyperbolic components are introduced and hyperbolic spinor representation of the curve (spacelike or timelike) in Minkowski space is expressed. Then, the fundamental theorem of differential geometry has been restated by means of these hyperbolic spinors. Finally, some examples about this study are given.
Keywords
Subject Classifications
15A6651B20
References
FrancescoAntonuccio, Hyperbolic Numbers and the Dirac Spinor, arXiv:hep-th/9812036v1 , ( 1998 ). MustafaBilici and MustafaÇalişkan, On the Involutes of the Spacelike Curve with a Timelike Binormal in Minkowski 3-Space , International Mathematical Forum, Vol. 4 , Number 31 , 1497 – ;1530 ( 2009 ). RichardBrauer and HermannWeyl, Spinors in n—dimensions , American Journal of Mathematics, Vol. 57 Number 2 , 425 – 449 ( 1935 ). doi: 10.2307/2371218 MosheCarmeli, 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 . ElieCartan, The theory of spinors, Dover , New York, 1981 . Abdullah AzizErgin, Timelike Darboux curves on a timelike surface M C M , Hadronic Journal, Vol. 24 , Number 6 , 701 – 712 ( 2001 ). Gerardo Francisco Torres delCastillo and Guadalupe SanchezBarrales, Spinor formulation of the differential geometry of curves , Revista Colombiana de Matematicas, Vol. 38 Number 1 , 27 – 34 ( 2004 ). ToshihikoIkawa, On curves and submanifolds in an indefinite-Riemannian manifold , Tsukuba Journal of Mathematics, Vol. 9 Number 2 , 353 – 371 ( 1985 ). IlimKisi and MuratTosun, Spinor Darboux Equations of Curves in Euclidean 3-Space , Mathematica Moravica, Vol. 19 Number 1 , 8793 ( 2015 ). Michel AngeLancret, Memoire sur les courbes a double courbure , Mémoires presentes a l'Institut par divers Savants , Vol 2 , Number 1 416 – 454 ( 1806 ). BarrettO'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press , New York, 1983 . MustafaOzdemir and Abdullah AzizErgin, Spacelike Darboux curves in Minkowski 3-space , Differential Geometry - Dynamical Systems, Vol. 9 , 131 – 137 ( 2007 ). ManfredoPerdigào do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, NJ , 1976 . David H.Sattinger and Oliver L.Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, Springer-Verlag , New York, 1986 . Dirk JanStruik, Lectures on Classical Differential Geometry, Dover , New-York, 1988 . DoganÜnal, IlimKisi and MuratTosun, Spinor Bishop Equation of Curves in Euclidean 3-Space , Advances in Applied Clifford Algebras, Vol. 23 Number 3 , 757 – 765 ( 2013 ). doi: 10.1007/s00006-013-0390-8 Maria DinaVivarelli, Development of Spinors Descriptions of Rotational Mechanics from Euler's Rigid Body Displacement Theorem , Celestial MechanicsVol. 32 , 193 – 207 ( 1984 ). doi: 10.1007/BF01236599 Isaak MoiseevichYaglom, A Simple non-Euclidean Geometry and its Physical Basis, Springer-Verlag , New-York, 1979 .
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