Surfaces family with common null asymptotic

Abstract

We analyzed the problem of finding a surfaces family through an asymptotic curve with Carton frame. We obtain the parametric representation for surfaces family whose members have the same as an asymptotic curve. By using the Cartan frame of the given null curve, we present the surface as a linear combination of this frame and analyzed the necessary and sufficient condition for that curve to satisfy the asymptotic requirement We illustrate the method by giving some examples. (C) 2015 Elsevier Inc. All rights reserved.