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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we give an example to support the main results.
📌 3 Key Takeaways
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Objective & Hypothesis:This article deals with the isomorphism between unit dual sphere, DS^2, and the subset of the tangent bundle of unit 2-sphere, TM ̅.
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Key Findings & Data:Study mapping, a ruled surface in〖 R〗^3corresponds to each curve on DS^2.
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Conclusion & Impact:Finally, we give an example to support the main results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Natural lift · Tangent bundle · Unit dual sphere
Abstract
This article deals with the isomorphism between unit dual sphere, DS^2, and the subset of the tangent bundle of unit 2-sphere, TM ̅. According to E. Study mapping, a ruled surface in〖 R〗^3corresponds to each curve on DS^2. Through this correspondence, a unique ruled surface in R^3is corresponded to natural lift curve on TM ̅. Then striction curve, shape operator, mean curvature and Gaussian curvature of these ruled surfaces obtained by the natural lift curves are calculated. Developabilitiy condition of these ruled surfaces is given. Finally, we give an example to support the main results.
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Cite This Article
Karaca, E., Çalışkan, M. (2020). Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves. Gazi University Journal of Science, Volume: 33 Issue: 3. https://doi.org/10.35378/gujs.588496