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Journals / Gazi University Journal of Science / 2020 / Cilt: 33 - Sayı: 3

Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves

Mustafa CALISKAN
Emel KARACA
Pages
751–759
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

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

Finally, we give an exampleto support the main results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article deals with the isomorphism between unit dual sphere, 𝐷𝑆2, and the subset of thetangent bundle of unit 2-sphere, 𝑇𝑀 ̅ .
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Key Findings & Data:Study mapping, a ruled surfacein ℝ3corresponds to each curve on 𝐷𝑆2.
💡
Conclusion & Impact:Finally, we give an exampleto support the main results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This article deals with the isomorphism between unit dual sphere, 𝐷𝑆2, and the subset of thetangent bundle of unit 2-sphere, 𝑇𝑀 ̅ . According to E. Study mapping, a ruled surfacein ℝ3corresponds to each curve on 𝐷𝑆2. Through this correspondence, a unique ruled surface inℝ3is corresponded to natural lift curve on 𝑇𝑀 ̅. Then striction curve, shape operator, meancurvature and Gaussian curvature of these ruled surfaces obtained by the natural lift curves arecalculated. Developabilitiy condition of these ruled surfaces is given. Finally, we give an exampleto support the main results.

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Cite This Article

CALISKAN, M., KARACA, E. (2022). Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves. Gazi University Journal of Science, Cilt: 33 - Sayı: 3, 751–759. https://ajindex.com/articles/521292

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