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Journals / International Electronic Journal of Geometry / 2026 / Volume: 15 Issue: 1

Family of Surfaces with a Common Special Involute and Evolute Curves

Süleyman Şenyurt(ORDU UNIVERSITY)0000-0003-1097-5541
Kebire Hilal Ayvacı(ORDU UNIVERSITY)0000-0002-5114-5475
Davut Canlı(ORDU UNIVERSITY)0000-0003-0405-9969
Pages
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Publication Date
2022-04-30
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AI Summary & Key Takeaways

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

Finally, we provide a set of examples to illustrate the corresponding surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define the necessary and sufficient conditions for a parametric surface on which both the involute and evolute of any given curve lie to be geodesic, asymptotic and curvature line.
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Key Findings & Data:Then, the first and second fundamental forms of these surfaces are calculated.
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Conclusion & Impact:Finally, we provide a set of examples to illustrate the corresponding surfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Geodesic curve · involue-evolute curves · asymptoticity

Abstract

In this paper, we define the necessary and sufficient conditions for a parametric surface on which both the involute and evolute of any given curve lie to be geodesic, asymptotic and curvature line. Then, the first and second fundamental forms of these surfaces are calculated. By using the Gaussian and mean curvatures, the developability and minimality assumptions are drawn, as well. Moreover we extended the idea to the ruled surfaces. Finally, we provide a set of examples to illustrate the corresponding surfaces.

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Cite This Article

Şenyurt, S., Ayvacı, K. H., Canlı, D. (2022). Family of Surfaces with a Common Special Involute and Evolute Curves. International Electronic Journal of Geometry, Volume: 15 Issue: 1. https://doi.org/10.36890/iejg.932757

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