Construction of Surface Pencil With a Given Spacelike Adjoint Curve

Abstract

The adjoint curve of any Frenet curve r=r(s) is defined as the integral of binormal vector with any parameter s, of a curve r. In this paper,we analyzed the problem of finding a surfaces pencil through a given the spacelike adjoint curve as an asymptotic curve, geodesic or a line of curvature in Minkowski 3-space, respectively. We find necessary and sufficient condition for a surface pencil possessing the spacelike adjoint curve as an asymptotic curve, geodesic or line of curvature. We illustrate this method by presenting some examples.