Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame

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 in terms of the rotation, element of , with the aid of the hyperbolic spinors.