An Examination for the Intersection of Two Ruled Surfaces

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Fundamental Journal of Mathematics and Applications
Volume:6 Issue:1
An Examination for the Intersection of Two Ruled Surfaces

An Examination for the Intersection of Two Ruled Surfaces

Pages : 70-77

View : 20 | Download : 9

Publication Date : 2023-03-29

Article Type : Research Paper

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 $\\lambdainsert ignore into journalissuearticles values(u,v);=0.$ Then, all redundant and non-redundant solutions of the zero-set are investigated. Furthermore, the degenerate situations $insert ignore into journalissuearticles values(u,v);=0$, where the whole plane is degenerated by the zero-set, are denoted. Finally, some examples are given to verify the results.
Keywords : Ruled surface, Surface intersection, Tangent bundle

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