Designing Generalized Cylinder with Characteristic Base Curve in Euclidean 3-space

Abstract

Designing a surface from a given curve under some special conditions is an important problem in many practical applications. The purpose of this article is to design a generalized cylinder whose base curve is a characteristic curve in Euclidean 3- space. The main results show that the generalized cylinder with geodesic, line of curvature, or asymptotic base curve is a rectifying cylinder, a right cylinder, or a plane respectively.