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Bishop Çatısı ile İlişkilendirilmiş Hasimoto Yüzeyleri

Year 2019, Volume: 9 Issue: 1, 13 - 22, 28.06.2019

Alev Kelleci Mehmet Bektaş Mahmut Ergüt

Abstract

Bu çalışmada Öklidyen 3-uzayındaki Hasimoto yüzeyleri
incelenmiştir. İlk olarak, Öklidyen 3-uzayındaki Hasimoto yüzeylerinin
geometrik özellikleri incelenmiştir. Özellikle Bishop çatısı ile ilişkilendirilmiş
bu yüzeylerin eğrilikleri elde edilmiştir. Daha sonrasında bu yüzeylerin Bishop
çatısına göre parametre eğrilerinin bazı karakterizasyonları verilmiştir.

Keywords

Hasimoto yüzeyler Duman halkası denklemi Bishop çatısı

References

  • Referans1 Rogers C., Schief W.K., Backlund and Darboux Transformations, Geometry of Modern Applications in Soliton Theory. Cambridge University Press (2002).
  • Referans2 Hasimoto H., A Soliton on a vortex …lament. J. Fluid. Mech. 51, 477–485 (1972).
  • Referans3 Erdoğdu M., Özdemir M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Math Phys Anal Geom (2014) 17:169–181.
  • Referans4 Bishop L.R., ”There is more than one way to frame a curve”, Amer. Math. Monthly, Volume 82,Issue 3, 246-251,1975.
  • Referans5 Bukcu B., Karacan, M. K., The Slant Helices According to Bishop Frame, World Academy of Science, Engineering and Technology Vol:3 2009- 11-20.
  • Referans6 Yılmaz S., Turgut M., A new version of Bishop frame and an application to spherical images, Journal of Mathematical Analysis and Applications, 371 (2010) 764–776.
  • Referans7 Inoguchi J., Binormal curves in Minkowski 3-space, IJMMS 21 (2003), 1365–1368.
  • Referans8 Eisenhart L. P., A Treatise On The Di¤erential Geometry Of Curves And Surfaces (1909).
  • Referans9 Da Rios L. S., On the motions of an unbounded ‡uid with a vortex filament of any shape, (in Italian), Rend. Circ. Mat. Palermo 22, 117 (1906).

The Hasimoto Surface According to Bishop Frame

Year 2019, Volume: 9 Issue: 1, 13 - 22, 28.06.2019

Alev Kelleci Mehmet Bektaş Mahmut Ergüt

Abstract

In this paper, we
investigate the Hasimoto surfaces in Euclidean 3- space. Firstly, we
investigate the geometric properties of these surfaces in Euclidean 3-space.
Especially, we obtain the curvatures of Hasimoto surface according to Bishop
frame. Then we give some characterization of parameter curves obtained
according to Bishop frame of Hasimoto surfaces.

Keywords

Hasimoto surface Smoke ring equation Bishop frame

References

  • Referans1 Rogers C., Schief W.K., Backlund and Darboux Transformations, Geometry of Modern Applications in Soliton Theory. Cambridge University Press (2002).
  • Referans2 Hasimoto H., A Soliton on a vortex …lament. J. Fluid. Mech. 51, 477–485 (1972).
  • Referans3 Erdoğdu M., Özdemir M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Math Phys Anal Geom (2014) 17:169–181.
  • Referans4 Bishop L.R., ”There is more than one way to frame a curve”, Amer. Math. Monthly, Volume 82,Issue 3, 246-251,1975.
  • Referans5 Bukcu B., Karacan, M. K., The Slant Helices According to Bishop Frame, World Academy of Science, Engineering and Technology Vol:3 2009- 11-20.
  • Referans6 Yılmaz S., Turgut M., A new version of Bishop frame and an application to spherical images, Journal of Mathematical Analysis and Applications, 371 (2010) 764–776.
  • Referans7 Inoguchi J., Binormal curves in Minkowski 3-space, IJMMS 21 (2003), 1365–1368.
  • Referans8 Eisenhart L. P., A Treatise On The Di¤erential Geometry Of Curves And Surfaces (1909).
  • Referans9 Da Rios L. S., On the motions of an unbounded ‡uid with a vortex filament of any shape, (in Italian), Rend. Circ. Mat. Palermo 22, 117 (1906).
There are 9 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Alev Kelleci

Mehmet Bektaş

Mahmut Ergüt This is me

Publication Date June 28, 2019
Submission Date June 2, 2018
Acceptance Date May 26, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

Cite

APA Kelleci, A., Bektaş, M., & Ergüt, M. (2019). The Hasimoto Surface According to Bishop Frame. Adıyaman University Journal of Science, 9(1), 13-22.
AMA Kelleci A, Bektaş M, Ergüt M. The Hasimoto Surface According to Bishop Frame. ADYU J SCI. June 2019;9(1):13-22.
Chicago Kelleci, Alev, Mehmet Bektaş, and Mahmut Ergüt. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science 9, no. 1 (June 2019): 13-22.
EndNote Kelleci A, Bektaş M, Ergüt M (June 1, 2019) The Hasimoto Surface According to Bishop Frame. Adıyaman University Journal of Science 9 1 13–22.
IEEE A. Kelleci, M. Bektaş, and M. Ergüt, “The Hasimoto Surface According to Bishop Frame”, ADYU J SCI, vol. 9, no. 1, pp. 13–22, 2019.
ISNAD Kelleci, Alev et al. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science 9/1 (June 2019), 13-22.
JAMA Kelleci A, Bektaş M, Ergüt M. The Hasimoto Surface According to Bishop Frame. ADYU J SCI. 2019;9:13–22.
MLA Kelleci, Alev et al. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science, vol. 9, no. 1, 2019, pp. 13-22.
Vancouver Kelleci A, Bektaş M, Ergüt M. The Hasimoto Surface According to Bishop Frame. ADYU J SCI. 2019;9(1):13-22.
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