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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 13 Issue: 1

Quaternionic and Dual Quaternionic Darboux Ruled Surfaces

Abdussamet Çalışkan(ORDU UNIVERSITY)0000-0002-1512-2452
Pages
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Publication Date
2021-06-30
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AI Summary & Key Takeaways

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

Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion.
📊
Key Findings & Data:Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated.
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Conclusion & Impact:Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Darboux vector · distribution parameter · dual spherical curve

Abstract

In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

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Cite This Article

Çalışkan, A. (2021). Quaternionic and Dual Quaternionic Darboux Ruled Surfaces. Turkish Journal of Mathematics and Computer Science, Volume: 13 Issue: 1. https://doi.org/10.47000/tjmcs.858793

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