On the evolute offsets of ruled surfaces using the Darboux frame

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume: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 : 46 | Download : 7

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :In this study, using Darboux frame {T,g,n} of ruled surface ϕinsert ignore into journalissuearticles values(s,v);, the evolute offsets ϕ^{∗}insert ignore into journalissuearticles values(s,v); with Darboux frame {T^{∗},g^{∗},n^{∗}} of ϕinsert ignore into journalissuearticles values(s,v); are defined. Characteristic properties of ϕ^{∗}insert ignore into journalissuearticles values(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 ϕinsert ignore into journalissuearticles values(s,v);, H^{∗}={T^{∗},g^{∗},n^{∗}} be the moving space along the base curve of ϕ^{∗}insert ignore into journalissuearticles values(s,v);, H′ and H^{∗′} be fixed Euclidean spaces.
Keywords : Darboux frame, evolute offset, ruled surface

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