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2021•Journal of Interdisciplinary MathematicsRequires access

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

Münevver Yıldırım Yılmaz, Zühal Küçükarslan Yüzbaşı

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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).

About this research paper

What this paper is about

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).

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Available 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).

Key concepts: Frenet–Serret formulas, Stable curve, Torsion of a curve, Pencil (optics), Mathematics, Surface (topology), Type (biology), Osculating circle

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