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

TL;DR

This paper introduces a new type of surface curve called the new D-type special curve in Galilean space, explores its properties, and provides conditions for its characterization, including visualizations of related surface families.

Contribution

It defines and analyzes the new D-type special curve, showing it generalizes geodesic and asymptotic curves, with conditions derived using Frenet frames in Galilean space.

Findings

The new D-type special curve is more general than geodesic and asymptotic curves.

Necessary and sufficient conditions for the curve are established.

Visual examples of the surface pencil are provided.

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).