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

       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.   

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

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. 

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  • 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.