On a Surface Pencil with a Common New Type of Special Suface Curve in Galilean Space G3

Abstract

In this study, we investigate a new type of a surface curve called a new D-type special curve. Also, we show that this special curve is more generally than a geodesic curve or an asymptotic curve. Then, we give the necessary and sufficient conditions for a curve to be the new D-type special curve using Frenet frame in Galilean space. We investigate some corollaries by taking account of a new D-type special curve as a helix, a salkowski and an anti-salkowski. After all, for the sake of visualizing of this study, we plot some examples for this surface pencil (i.e. surface family).