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Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame

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Abstract

In this paper, we study to express the theory of curves including a wide section of Lorentzian geometry in terms of spinors with two hyperbolic components which has an important place in the Clifford algebra. In other words, we express the rotation, element of SO(1, 3), between the Frenet frame and the other frame defined as alternatively of the (spacelike or timelike) curves in Minkowski space \({\mathbb{R}_1^3}\) in terms of the rotation, element of \({SU(2,\mathbb{H})}\), with the aid of the hyperbolic spinors.

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Authors and Affiliations

  1. Department of Mathematics, Sakarya University, Sakarya, 54187, Turkey

    Tülay Erişir, Mehmet Ali Güngör & Murat Tosun

  2. Faculty of Engineering and Natural Sciences, International University of Sarajevo, 71210, Sarajevo, Bosnia and Herzegovina

    Mehmet Ali Güngör

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  1. Tülay Erişir
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  2. Mehmet Ali Güngör
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  3. Murat Tosun
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Correspondence to Tülay Erişir.

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Erişir, T., Ali Güngör, M. & Tosun, M. Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame. Adv. Appl. Clifford Algebras 25, 799–810 (2015). https://doi.org/10.1007/s00006-015-0552-y

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  • DOI: https://doi.org/10.1007/s00006-015-0552-y

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