Tangent bundle of pseudo-sphere and Non-null slant ruled surfaces

Abstract

A unique type of ruled surface called a slant ruled surface has some fixed directions in the space and Frenet vectors that form a constant angle with one another. In this study, we construct the novel approximation for this slant ruled surface, also known as a non-null slant ruled surface, which was obtained by the striction curve of the natural lift curve. The relationship between the slant ruled surfaces acquired by the striction curves of the natural lift curves and pseudo-spheres is then derived via E. Study mapping. Furthermore, the striction curves of the natural lift curves in $E^{3}_{1}$ are used to classify as $\vec{\bar{q}}-,\vec{\bar{h}}-,\vec{\bar{a}}-$ spacelike (resp., timelike) slant ruled surfaces. We also provide some additional cases that may illustrate the important results.