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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 52 Issue: 4

Concircular helices and concircular surfaces in Euclidean 3-space $\mathbb{R}^{3}$

Pascual Lucas(Universidad de Murcia)0000-0002-4354-9736
José Antonio Ortega Yagües(Universidad de Murcia)0000-0001-9521-1051
Pages
—
Publication Date
2023-08-15
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AI Summary & Key Takeaways

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

Finally, we characterize the concircular helices as geodesics of concircular surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we characterize concircular helices in $\mathbb{R}^{3}$ by means of a differential equation involving their curvature and torsion.
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Key Findings & Data:We find a full description of concircular surfaces in $\mathbb{R}^{3}$ as a special family of ruled surfaces, and we show that $M\subset\mathbb{R}^{3}$ is a proper concircular surface if and only if either $M$ is parallel to a conical surface or $M$ is the normal surface to a spherical curve.
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Conclusion & Impact:Finally, we characterize the concircular helices as geodesics of concircular surfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:generalized helix · slant helix · rectifying curve

Abstract

In this paper we characterize concircular helices in $\mathbb{R}^{3}$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $\mathbb{R}^{3}$ as a special family of ruled surfaces, and we show that $M\subset\mathbb{R}^{3}$ is a proper concircular surface if and only if either $M$ is parallel to a conical surface or $M$ is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.

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Cite This Article

Lucas, P., Yagües, J. A. O. (2023). Concircular helices and concircular surfaces in Euclidean 3-space $\mathbb{R}^{3}$. Hacettepe Journal of Mathematics and Statistics, Volume: 52 Issue: 4. https://doi.org/10.15672/hujms.1187220

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