A Surface Family with a Common Asymptotic Curve in the Euclidean 3-Space

Rashad A. Abdel-Baky


In this paper, we offer an approach for study the problem on how to construct a surface family from a given asymptotic curve and we deduce the necessary and sufficient condition for the given curve to be the asymptotic curve for the parametric surface. Meanwhile, some representative curves are chosen to construct the corresponding surfaces which possess these curves as asymptotic curves. The extension to ruled and developable surfaces is also outlined. Finally, we demonstrated some interesting ruled and developable surfaces about the subject.

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