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

Authors : Nabil ALTHİBANY

Pages : 61-70

View : 21 | Download : 6

Publication Date : 2021-09-30

Article Type : Research Paper

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