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 R 3 1 in terms of the rotation, element of SU (2, H), with the aid of the hyperbolic spinors.Mathematics Subject Classification. 62J05, 62J07.

Pedal Curves of Non-Lightlike Curves in Minkowski 3-Space

“…A lot of scholars are interested in geometric objects with symmetry in different spaces, and they study the different properties of them (cf. [7][8][9][10]).…”

E_1^3 3-Boyutlu Lorentz Uzayda Spinor Q-Denklemleri

“…Geometrical studies of the notion spinors were taken into consideration as in the following works. By means of hyperbolic spinor representation stemmed from the different structure of Lorentz 3-space, non-null regular curves were characterized in the research [7]. The spinor analysis of Darboux frame for non-null curves lying in non-degenerate surface was given in the same space by the work [8].…”

Spinor Equations of Successor Curves

“…In another study, spinor formulation of Bertrand curves was given [8]. Moreover, the spinor formulations of some special curves in three-dimensional Minkowski space were obtained based on these studies in three-dimensional Euclidean space [1,6,9]. In this study, a curve (α) with unit speed and a successor curve (β ) with the same arc-length parameter of the curve (α) have been considered.…”