Surface Family with a Common Asymptotic Curve in Minkowski 3-Space

Abstract

In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.