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Journals / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 2

Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space

Bülent ALTUNKAYA
Pages
229–240
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

After that, we characterize rectifying slant helices which are geodesics of 2n-dimensional cone.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we study slant helices in the n-dimensional Euclidean space.
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Key Findings & Data:By means of these methods, first we characterize slant helices and Salkowski curves which lie on 2n-dimensional hyperboloid.
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Conclusion & Impact:After that, we characterize rectifying slant helices which are geodesics of 2n-dimensional cone.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Slant helix · Salkowski curve · rectifying curve

Abstract

In this work, we study slant helices in the n-dimensional Euclidean space. We give methods to determine the position vectors of slant helices from arclength parameterized curves that lie on the unit hypersphere. By means of these methods, first we characterize slant helices and Salkowski curves which lie on 2n-dimensional hyperboloid. After that, we characterize rectifying slant helices which are geodesics of 2n-dimensional cone.

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Cite This Article

ALTUNKAYA, B. (2022). Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space. International Electronic Journal of Geometry, Cilt: 12 - Sayı: 2, 229–240. https://ajindex.com/articles/539642

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