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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

On the evolute offsets of ruled surfaces using the Darboux frame

Gülsüm Yeliz Şentürk0000-0002-8647-1801
Salim Yüce0000-0002-8296-6495
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Yayın Tarihi
2019-08-01
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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.

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:Characteristic properties of ϕ^{∗}(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Darboux frame · evolute offset · ruled surface

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.

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Bu Makaleye Atıf Yap

Şentürk, G. Y., Yüce, S. (2019). On the evolute offsets of ruled surfaces using the Darboux frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.516604

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Kaynakça (10)

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