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Journals / Sakarya University Journal of Science / 2018 / Cilt: 22 Sayı: 6

On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame

Mustafa YENEROĞLU
Pages
1770–1773
Publication Date
2018-12-01
DOI
—
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AI Summary & Key Takeaways

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

Finally, in case of having a flow of developable surface is inextensible we prove that this surface is not minimal.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate inextensible flows of focal curves in Euclidean 3-space associated to developable surfaces to ribbon frame.
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Key Findings & Data:We present some new generalizations for torsion and curvature of focal curves in associated to developable surfaces.
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Conclusion & Impact:Finally, in case of having a flow of developable surface is inextensible we prove that this surface is not minimal.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Developable surface · inextensible flows · Developable surface

Abstract

In this paper, we investigate inextensible flows of focal curves in Euclidean 3-space associated to developable surfaces to ribbon frame. We present some new generalizations for torsion and curvature of focal curves in associated to developable surfaces. Finally, in case of having a flow of developable surface is inextensible we prove that this surface is not minimal.

Özet

Bu makalede, ribbon çatılı açılabilir yüzeylerle birleştirilmiş Öklidyen 3-uzayda fokal eğrilerin inextensible flows larını araştıracağız. Açılabilir yüzeylerle birleştirilmiş de fokal eğrilerin torsiyon ve eğriliği için bazı yeni genelleştirmeler sunacağız. Sonuçta, açılabilir yüzeyin bir flow nun inextensible olması durumunda yüzeyin minimal olmadığını ispatlayacağız.

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Cite This Article

YENEROĞLU, M. (2018). On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. Sakarya University Journal of Science, Cilt: 22 Sayı: 6, 1770–1773. https://ajindex.com/articles/942099

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References (1)

  1. REFERENCES [1] P. Alegre, K. Arslan, A. Carriazo, C. Murathan and G. Öztürk, Some Special Types of Developable Ruled Surface, Hacettepe Journal of Mathematics and Statistics, Vol. 39 No.3, pp. 319-325, 2010. [2] R. Uribe-Vargas, On vertices, focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc. Vol. 36 No. 3, 285—307, 2005. [3] T. Korpinar, E. Turhan and G. Altay,Inextensible flows of developable surfaces associated focal curve of helices in Euclidean 3-space E3, Acta Universitatis Apulensis, Vol. 29, pp. 235-240, 2012. [4] J. Bohr and S. Markvorsen, Ribbon Crystals, Plos one, 8 (10) (2013). [5] M. Yeneroglu, New focal curves according to ribbon frame, Prespacetime Journal, Vol. 7 No. 5, 2016. [6] D.Y. Kwon, F.C. Park and D.P. Chi, Inextensible flows of curves and developable surfaces, Applied Math. Letters, Vol. 18 No. 10, 1156-1162, 2005. [7] L. Giomi, L. Mahadevan, Statistical mechanics of developable ribbons, Phys. Rev. Lett., Vol. 104, 2010. [8] D. E. Blair: Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Springer-Verlag 509, Berlin-New York, 1976. [9] M.P. Carmo: Differential Geometry of Curves and Surfaces, Pearson Education, 1976.