Araştırma Makalesi
Yıl 2019,
Cilt: 9 Sayı: 1, 13 - 22, 28.06.2019
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
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, 477485 (1972).
- Referans3 Erdoğdu M., Özdemir M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Math Phys Anal Geom (2014) 17:169181.
- 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) 764776.
- Referans7 Inoguchi J., Binormal curves in Minkowski 3-space, IJMMS 21 (2003), 13651368.
- 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).
Yıl 2019,
Cilt: 9 Sayı: 1, 13 - 22, 28.06.2019
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
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, 477485 (1972).
- Referans3 Erdoğdu M., Özdemir M., Geometry of Hasimoto Surfaces in Minkowski 3-Space, Math Phys Anal Geom (2014) 17:169181.
- 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) 764776.
- Referans7 Inoguchi J., Binormal curves in Minkowski 3-space, IJMMS 21 (2003), 13651368.
- 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 | |
| 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
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