- Journal of New Theory
- Issue: 37
- Generating Generalized Cylinder with Geodesic Base Curve According to Darboux Frame
Generating Generalized Cylinder with Geodesic Base Curve According to Darboux Frame
Authors : Nabil Althibany
Pages : 99-107
Doi:10.53570/jnt.1036307
View : 14 | Download : 6
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