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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 3

Some Characterizations of Slant Helices in the Euclidean Space En

SOME CHARACTERIZATIONS OF SLANT HELICES IN THE EUCLIDEAN SPACE En

Ahmad T. ALİ
Melih TURGUT
Pages
327–336
Publication Date
2010-03-01
DOI
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AI Summary & Key Takeaways

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

Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, the notion of a slant helix is extended to the space En First, we introduce the type-2 harmonic curvatures of a regular curve.Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space.
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Key Findings & Data:We also express some integral characterizations of such curves in terms of the curvature functions.
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Conclusion & Impact:Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Euclidean n-space · Frenet equations · Slant helices

Abstract

In this work, the notion of a slant helix is extended to the space En First, we introduce the type-2 harmonic curvatures of a regular curve.Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.

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Cite This Article

ALİ, A. T., TURGUT, M. (2010). Some Characterizations of Slant Helices in the Euclidean Space En. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 3, 327–336. https://ajindex.com/articles/669744

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