On a surface pencil with a common new type of special surface curve in Galilean space G₃

Abstract

In this study, we investigate a new type of surface curve called a D-type special curve. We also show that this special curve is more general 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. Moreover, we investigate some results by taking account of a D-type special curve as a helix, a Salkowski curve and an anti-Salkowski curve. After then, for the sake of visualizing this study, we plot some examples for this surface pencil (i.e. surface family).

Subject Classification: (2010):

• 53A35

Keywords:

• New D-type special curve
• Geodesic curve
• Isoparametric curve
• Parametric surface
• Galilean space