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

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

Mustafa DÜLDÜL
Pages
274–283
Publication Date
2020-01-20
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space.
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Key Findings & Data: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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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

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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References (9)

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