- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- On the evolute offsets of ruled surfaces using the Darboux frame
On the evolute offsets of ruled surfaces using the Darboux frame
Authors : Gülsüm Yeliz Şentürk, Salim Yüce
Pages : 1256-1264
Doi:10.31801/cfsuasmas.516604
View : 20 | Download : 4
Publication Date : 2019-08-01
Article Type : Research
Abstract :In this study, using Darboux frame {T,g,n} of ruled surface ϕ(s,v), the evolute offsets ϕ^{∗}(s,v) with Darboux frame {T^{∗},g^{∗},n^{∗}} of ϕ(s,v) are defined. Characteristic properties of ϕ^{∗}(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces ϕ_{T^{∗}}^{∗},ϕ_{g^{∗}}^{∗} and ϕ_{n^{∗}}^{∗} are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfaffian vectors of motions H/H′ and H^{∗}/H^{∗′}, where H={T,g,n} be the moving space along the base curve of ϕ(s,v), H^{∗}={T^{∗},g^{∗},n^{∗}} be the moving space along the base curve of ϕ^{∗}(s,v), H′ and H^{∗′} be fixed Euclidean spaces.Keywords : Darboux frame, evolute offset, ruled surface