Spinors corresponding to modified orthogonal frames in Euclidean 3-space

Abstract

The space of spinors, defined as the basic representation of a Clifford algebra, can be expressed as the spin representation of an orthogonal Lie algebra. At the same time, these spin representations can also be characterized as finite-dimensional projective representations of the special orthogonal group. From a geometrical perspective, the behavior of spinors under the action of Lie groups can be examined. Thus, one has the advantage of making a concrete and basic explanation about what spinors are in a geometrical sense. In this study, the spinor representations of an orthogonal frame moving on a analytic curve is investigated geometrically. The spinor equations corresponding to a modified orthogonal frame and a modified orthogonal frame with \(\tau\) are derived. The relations between modified orthogonal frames and the Frenet frame are established regarding their spinor formulations. Our motivation in this paper is to give spinor representations of the modified orthogonal frame. Consequently, this study has been planned as an interdisciplinary study between Clifford algebras and geometry.