Advances in Applied Clifford Algebras

, Volume 25, Issue 4, pp 799–810 | Cite as

Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame

  • Tülay Erişir
  • Mehmet Ali Güngör
  • Murat Tosun


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.

Mathematics Subject Classification

62J05 62J07 


Clifford algebra Hyperbolic spinors Alternative frame Minkowski space 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Tülay Erişir
    • 1
  • Mehmet Ali Güngör
    • 1
    • 2
  • Murat Tosun
    • 1
  1. 1.Department of MathematicsSakarya UniversitySakaryaTurkey
  2. 2.Faculty of Engineering and Natural SciencesInternational University of SarajevoSarajevoBosnia and Herzegovina

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