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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 ${\mathbb{R}}^3_1$. 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.
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참고문헌 (21)
참고문헌 신청
F. Antonuccio / 1998 / Hyperbolic Numbers and the Dirac Spinor / arXiv:hepth/9812036v1
M. Carmeli / 1977 / Group Theory and General Relativity, Representations of the Lorentz Group and Their Applications to the Gravitational Field / McGraw-Hill, Imperial College Press
E. Cartan / 1981 / The theory of spinors / Dover
G. F. T. Del Castillo / 2009 / Spinors in Four-Dimensional Spaces / Springer
G. F. T. Del Castillo / 2004 / Spinor formulation of the differential geometry of curves / Revista Colombiana de Matematicas 38:27~34
M. Carmeli / 1977 / Group Theory and General Relativity, Representations of the Lorentz Group and Their Applications to the Gravitational Field / McGraw-Hill, Imperial College Press
E. Cartan / 1981 / The theory of spinors / Dover
G. F. T. Del Castillo / 2009 / Spinors in Four-Dimensional Spaces / Springer
G. F. T. Del Castillo / 2004 / Spinor formulation of the differential geometry of curves / Revista Colombiana de Matematicas 38:27~34
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