Hyperbolic Spinor Representations of Non-Null Framed Curves

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.Comment: 28 pages, 2 figure

ON FRAMED TZITZEICA CURVES IN EUCLIDEAN SPACE

Investigations are very important for non-regular curves in differential geometry. Framed curves have been used recently to study singular curves, and they have many contributions to singularity theory. In this study, framed Tzitzeica curves are introduced with the help of framed curves. In addition, some framed special curves that satisfy the Tzitzeica condition are given. New results have been obtained among the framed curves of these curves