Generating Generalized Cylinder with Geodesic Base Curve According to Darboux Frame

Authors : Nabil Althibany

Pages : 99-107

Doi:10.53570/jnt.1036307

View : 19 | Download : 8

Publication Date : 2021-12-31

Article Type : Research

Abstract :This paper aims to design a generalized cylinder with a geodesic base curve according to the Darboux frame in Euclidean 3-space. A generalized cylinder is a special ruled surface that is constructed by a continuous fixed motion of a generator line called the ruling along a given curve called the base curve. The necessary and sufficient conditions for the base curve to be geodesic are studied. The main results show that the generalized cylinder with a geodesic base curve is an osculating cylinder whose base curve is a helical geodesic, and the rulings are directed by the unit osculating Darboux vector.
Keywords : Generalized cylinder, geodesic, Darboux frame, general helix, osculating Darboux vector