Surfaces Family with Common Smarandache Geodesic Curve

Abstract

In this paper, we analyzed the problem of finding a surfaces family through a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we constructed a differential equation system such that a given Smarandache curves satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, we demonstrated some interesting surfaces about subject.