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Dergiler / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 1

Vector fields and planes in E4 which play the role of Darboux vector

Mustafa DÜLDÜL
Sayfa
274–283
Yayın Tarihi
2020-01-20
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base curve is always a geodesic on the developable one.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space.
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Temel Bulgular & Veri:We also show that, contrary to their definitions, osculating curves of the first kind and rectifying curves in Euclidean 4-space can be considered as space curves whose position vectors always lie in a two-dimensional subspace.
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Sonuç & Katkı:Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base curve is always a geodesic on the developable one.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Darboux vector · vector field · ruled hypersurface

Abstract

In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space. By using these vector fields we determine some new planes, curves, and ruled hypersurfaces. We show that the determined new planes play the role of the Darboux vector. We also show that, contrary to their definitions, osculating curves of the first kind and rectifying curves in Euclidean 4-space can be considered as space curves whose position vectors always lie in a two-dimensional subspace. Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base curve is always a geodesic on the developable one.

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Bu Makaleye Atıf Yap

DÜLDÜL, M. (2020). Vector fields and planes in E4 which play the role of Darboux vector. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 1, 274–283. https://ajindex.com/articles/193224

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Kaynakça (9)

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