An Examination for the Intersection of Two Ruled Surfaces

Abstract

In this study, firstly, each natural lift curve of the main curve is corresponded to the ruled surface by exploiting E. Study mapping and the relation among the subset of the tangent bundle of unit 2-sphere, $T\bar{M}$ and ruled surfaces in $\mathbb{R}^{3}$. Secondly, the intersection of two ruled surfaces, which are obtained by using the relation given above, is examined for the condition of the zero-set of $\lambda(u,v)=0.$ Then, all redundant and non-redundant solutions of the zero-set are investigated. Furthermore, the degenerate situations $(u,v)=0$, where the whole plane is degenerated by the zero-set, are denoted. Finally, some examples are given to verify the results.