Classification of Ruled Surfaces Family with Common Characteristic Curve in Euclidean 3-space

Year 2021, Volume: 6 Issue: 2, 61 - 70, 30.09.2021

Nabil Althibany

Abstract

Classification of ruled surfaces that satisfying certain geometric conditions has been studied
by many researchers in the past years. The purpose of this paper is to study and classify the family of ruled
surfaces whose common directrix satisfies the requirements of characteristic curves in three-dimensional
Euclidean space. The family of ruled surfaces is parameterized by its directrix curve and director vector
that is expressed by a linear combination of Frenet frame with angular functions as coefficients. According
to the type of characteristic directrix curve, the family of ruled surfaces is classified into three types, and
one type when the family is developable.

Keywords

Ruled surfaces family, Characterstic curve, Classification

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