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

Year 2018, Volume: 22 Issue: 6, 1770 - 1773, 01.12.2018
https://doi.org/10.16984/saufenbilder.331028

Abstract

       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.

 


 

References

  • 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.

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

Year 2018, Volume: 22 Issue: 6, 1770 - 1773, 01.12.2018
https://doi.org/10.16984/saufenbilder.331028

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.

 

References

  • 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.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mustafa Yeneroğlu

Publication Date December 1, 2018
Submission Date July 26, 2017
Acceptance Date May 29, 2018
Published in Issue Year 2018 Volume: 22 Issue: 6

Cite

APA Yeneroğlu, M. (2018). On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. Sakarya University Journal of Science, 22(6), 1770-1773. https://doi.org/10.16984/saufenbilder.331028
AMA Yeneroğlu M. On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. SAUJS. December 2018;22(6):1770-1773. doi:10.16984/saufenbilder.331028
Chicago Yeneroğlu, Mustafa. “On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1770-73. https://doi.org/10.16984/saufenbilder.331028.
EndNote Yeneroğlu M (December 1, 2018) On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. Sakarya University Journal of Science 22 6 1770–1773.
IEEE M. Yeneroğlu, “On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame”, SAUJS, vol. 22, no. 6, pp. 1770–1773, 2018, doi: 10.16984/saufenbilder.331028.
ISNAD Yeneroğlu, Mustafa. “On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame”. Sakarya University Journal of Science 22/6 (December 2018), 1770-1773. https://doi.org/10.16984/saufenbilder.331028.
JAMA Yeneroğlu M. On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. SAUJS. 2018;22:1770–1773.
MLA Yeneroğlu, Mustafa. “On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1770-3, doi:10.16984/saufenbilder.331028.
Vancouver Yeneroğlu M. On Inextensible Flows Developable Surfaces Associated Focal Curve According to Ribbon Frame. SAUJS. 2018;22(6):1770-3.