Surfaces Family with Common Smarandache Asymptotic Curve According to Bishop Frame in Euclidean Space

Abstract

In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve. © Soc. Paran. de Mat.