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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 4

Constructions of helicoidal surfaces by using curvature functions in isotropic space

Dae Won Yoon0000-0001-8620-0676
Jae Won Lee0000-0001-8562-0767
Chul Woo Lee0000-0003-0223-2318
Pages
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Publication Date
2019-08-08
DOI
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AI Summary & Key Takeaways

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

Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions.
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Key Findings & Data:In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions.
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Conclusion & Impact:Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Isotropic space · helicoidal surface · mean curvature

Abstract

In the present  paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct  helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions. Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.

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Cite This Article

Yoon, D. W., Lee, J. W., Lee, C. W. (2019). Constructions of helicoidal surfaces by using curvature functions in isotropic space. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 4. https://ajindex.com/articles/1402754

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