Hyperbolic Spinor Representations of Non-Null Framed Curves

Abstract

In this paper, we intend to bring together the hyperbolic spinors, which are useful frameworks from mathematics to physics, and both spacelike and timelike framed curves in Minkowski 3-space $\mathbb{R}_1^3$, which are new type attractive frames and very crucial issue for singularity theory especially. First, we obtain new adapted frames which are called adapted frames for non-null (spacelike and timelike) framed curves in $\mathbb{R}_1^3$. Then, we investigate the hyperbolic spinor representations of non-null framed curves of the general and adapted frames. Also, we find some geometric results and interpretations with respect to them, and we obtain illustrative and numerical examples with figures in order to support the given theorems and results.