The Hasimoto Surface According to Bishop Frame

Ergüt, Mahmut; BEKTAŞ, Mehmet; Kelleci, Alev

The Hasimoto Surface According to Bishop Frame

Alev KELLECİ, (Fırat University, Faculty of Science, Department of Mathematics, Elazığ, Türkiye)

Mehmet BEKTAŞ, (Fırat University, Faculty of Science, Department of Mathematics, Elazığ, Türkiye)

Mahmut ERGÜT (Namık Kemal University, Faculty of Science and Letters, Department of Mathematics, Tekirdağ, Türkiye)

Adıyaman Üniversitesi Fen Bilimleri Dergisi

5 0

Yıl: 2019 Cilt: 9 Sayı: 1 Sayfa Aralığı: 13 - 22 Metin Dili: İngilizce İndeks Tarihi: 23-10-2019

The Hasimoto Surface According to Bishop Frame

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 Bishopframe of Hasimoto surfaces.

Anahtar Kelime:

Bishop Çatısı ile İlişkilendirilmiş Hasimoto Yüzeyleri

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 Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

Abdel-All, N. H., Hussien, R. A. and Youssef, T., Hasimoto Surfaces, Life Science Journal, 9(3), 556-560, 2012.
Bishop, L. R., There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82(3), 246-251, 1975.
Bukcu, B. and Karacan, M. K., The Slant Helices According to Bishop Frame, World Academy of Science, Engineering and Technology, 3, 11-20, 2009.
Çakmak, A., Parallel Surfaces of Hasimoto Surfaces in Euclidean 3-Space, BEÜ Journal of Science, 7(1), 125-132, 2018.
Da Rios, L. S., On the Motions of an Unbounded Fluid with a Vortex Filament of any Shape, Rend. Circ. Mat. Palermo, 22, 117, 1906.
Eisenhart, L. P., A Treatise on the Differential Geometry of Curves and Surfaces, Dover Publications, Inc. Mineola, New York, 1909.
Erdogdu, M. and Özdemir, M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Math. Phys. Anal. Geom., 17, 169-181, 2014.
Hasimoto, H., A Soliton on a Vortex Filament, J. Fluid. Mech., 51, 477-485 1972.
Rogers, C. and Schief, W. K., Backlund and Darboux Transformations, Geometry of Modern Applications in Soliton Theory, Cambridge University Press, 2002.
Yılmaz, S. and Turgut, M., A New Version of Bishop Frame and an Application to Spherical Images, J. Math. Anal. Appl., 371, 764-776, 2010.

APA	Kelleci A, BEKTAŞ M, Ergüt M (2019). The Hasimoto Surface According to Bishop Frame. , 13 - 22.
Chicago	Kelleci Alev,BEKTAŞ Mehmet,Ergüt Mahmut The Hasimoto Surface According to Bishop Frame. (2019): 13 - 22.
MLA	Kelleci Alev,BEKTAŞ Mehmet,Ergüt Mahmut The Hasimoto Surface According to Bishop Frame. , 2019, ss.13 - 22.
AMA	Kelleci A,BEKTAŞ M,Ergüt M The Hasimoto Surface According to Bishop Frame. . 2019; 13 - 22.
Vancouver	Kelleci A,BEKTAŞ M,Ergüt M The Hasimoto Surface According to Bishop Frame. . 2019; 13 - 22.
IEEE	Kelleci A,BEKTAŞ M,Ergüt M "The Hasimoto Surface According to Bishop Frame." , ss.13 - 22, 2019.
ISNAD	Kelleci, Alev vd. "The Hasimoto Surface According to Bishop Frame". (2019), 13-22.

APA	Kelleci A, BEKTAŞ M, Ergüt M (2019). The Hasimoto Surface According to Bishop Frame. Adıyaman Üniversitesi Fen Bilimleri Dergisi, 9(1), 13 - 22.
Chicago	Kelleci Alev,BEKTAŞ Mehmet,Ergüt Mahmut The Hasimoto Surface According to Bishop Frame. Adıyaman Üniversitesi Fen Bilimleri Dergisi 9, no.1 (2019): 13 - 22.
MLA	Kelleci Alev,BEKTAŞ Mehmet,Ergüt Mahmut The Hasimoto Surface According to Bishop Frame. Adıyaman Üniversitesi Fen Bilimleri Dergisi, vol.9, no.1, 2019, ss.13 - 22.
AMA	Kelleci A,BEKTAŞ M,Ergüt M The Hasimoto Surface According to Bishop Frame. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2019; 9(1): 13 - 22.
Vancouver	Kelleci A,BEKTAŞ M,Ergüt M The Hasimoto Surface According to Bishop Frame. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2019; 9(1): 13 - 22.
IEEE	Kelleci A,BEKTAŞ M,Ergüt M "The Hasimoto Surface According to Bishop Frame." Adıyaman Üniversitesi Fen Bilimleri Dergisi, 9, ss.13 - 22, 2019.
ISNAD	Kelleci, Alev vd. "The Hasimoto Surface According to Bishop Frame". Adıyaman Üniversitesi Fen Bilimleri Dergisi 9/1 (2019), 13-22.