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Bishop Çatısı ile İlişkilendirilmiş Hasimoto Yüzeyleri

Yıl 2019, Cilt: 9 Sayı: 1, 13 - 22, 28.06.2019

Alev Kelleci , Mehmet Bektaş , Mahmut Ergüt

Öz

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.

Anahtar Kelimeler

Hasimoto yüzeyler Duman halkası denklemi Bishop çatısı

Kaynakça

  • 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

Yıl 2019, Cilt: 9 Sayı: 1, 13 - 22, 28.06.2019

Alev Kelleci , Mehmet Bektaş , Mahmut Ergüt

Öz

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.

Anahtar Kelimeler

Hasimoto surface Smoke ring equation Bishop frame

Kaynakça

  • 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).
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Matematik
Yazarlar

Alev Kelleci

Mehmet Bektaş

Mahmut Ergüt Bu kişi benim

Yayımlanma Tarihi 28 Haziran 2019
Gönderilme Tarihi 2 Haziran 2018
Kabul Tarihi 26 Mayıs 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 1

Kaynak Göster

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. Haziran 2019;9(1):13-22.
Chicago Kelleci, Alev, Mehmet Bektaş, ve Mahmut Ergüt. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science 9, sy. 1 (Haziran 2019): 13-22.
EndNote Kelleci A, Bektaş M, Ergüt M (01 Haziran 2019) The Hasimoto Surface According to Bishop Frame. Adıyaman University Journal of Science 9 1 13–22.
IEEE A. Kelleci, M. Bektaş, ve M. Ergüt, “The Hasimoto Surface According to Bishop Frame”, ADYU J SCI, c. 9, sy. 1, ss. 13–22, 2019.
ISNAD Kelleci, Alev vd. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science 9/1 (Haziran 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 vd. “The Hasimoto Surface According to Bishop Frame”. Adıyaman University Journal of Science, c. 9, sy. 1, 2019, ss. 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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