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Yıl 2021, Cilt: 11 Sayı: 1, 87 - 100, 30.06.2021

Kemal Eren Alev Kelleci Akbay

https://doi.org/10.37094/adyujsci.820698
Cited By: 2

Öz

Kaynakça

  • [1] Sipus, Z.M., Vladimir, V., The harmonic evolute of a surface in Minkowski 3-space, Mathematical Communications, 19, 43-55, 2014.
  • [2] Lopez, R., Sipus, Z.M., Gajcic, L.P., Protrka, I., Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz-Minkowski space, International Journal of Geometric Methods in Modern Physics, 16 (5), 1950076, 2019.
  • [3] Körpinar, T., Kaymanli, G.U., On the harmonic evolute of quasi normal surfaces, Journal of Science and Arts, 1 (50), 55-64, 2020.
  • [4] Eren, K., Kösal, H.H., Evolution of space curves and the special ruled surfaces with modified orthogonal frame, AIMS Mathematics, 5 (3), 2027-2039, 2020.
  • [5] Kelleci, A., Eren, K., On evolution of some associated type ruled surfaces, Mathematical Sciences and Applications E-Notes, 8 (2), 178-186, 2020.
  • [6] Hasimoto, H., Motion of a vortex filament and its relation to elastica, Journal of the Physical Society of Japan, 31, 293-294, 1971.
  • [7] Hasimoto, H., A soliton on a vortex filament, Journal of Fluid Mechanics, 51 (3), 477-485, 1972.
  • [8] Rogers, C., Schief, W.K., Bäcklund and Darboux transformations, Cambridge University Press, 432, 2002.
  • [9] Abdel-All, N.H., Hussien, R.A., Youssef, T., Hasimoto surfaces, Life Science Journal, 9 (3), 556-560, 2012.
  • [10] Kelleci, A., Bektaş, M., Ergüt, M., The Hasimoto surface according to Bishop frame, Adıyaman University Journal of Science, 9 (1), 13-22, 2019.
  • [11] Erdoğdu, M., Özdemir, M., Geometry of Hasimoto surfaces in Minkowski 3-space, Mathematical Physics, Analysis and Geometry, 17, 169-181, 2014.
  • [12] Çakmak, A., Öklid 3-uzayında Hasimoto yüzeylerinin paralel yüzeyleri, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 7 (1), 125-132, 2018.

On the Harmonic Evolute Surfaces of Hasimoto Surfaces

Yıl 2021, Cilt: 11 Sayı: 1, 87 - 100, 30.06.2021

Kemal Eren Alev Kelleci Akbay

https://doi.org/10.37094/adyujsci.820698
Cited By: 2

Öz

In this study, firstly by considering the evolution of a moving space curve, we give some related definitions and some new results about Hasimoto surfaces in Euclidean 3-spaces. Secondly, we examine harmonic evolute surfaces of Hasimoto surfaces in Euclidean 3-spaces and also, we give some geometric properties of these type surfaces. Moreover, we express the properties of parameter curves of harmonic evolute surfaces in Euclidean space. Finally, we give an explicit example of Hasimoto surface and its harmonic evolute surface and also we plot these surfaces.

Anahtar Kelimeler

Hasimoto surfaces; harmonic evolute surface; binormal motion; evolution of curves and surfaces; Gaussian curvature; mean curvature.

Kaynakça

  • [1] Sipus, Z.M., Vladimir, V., The harmonic evolute of a surface in Minkowski 3-space, Mathematical Communications, 19, 43-55, 2014.
  • [2] Lopez, R., Sipus, Z.M., Gajcic, L.P., Protrka, I., Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz-Minkowski space, International Journal of Geometric Methods in Modern Physics, 16 (5), 1950076, 2019.
  • [3] Körpinar, T., Kaymanli, G.U., On the harmonic evolute of quasi normal surfaces, Journal of Science and Arts, 1 (50), 55-64, 2020.
  • [4] Eren, K., Kösal, H.H., Evolution of space curves and the special ruled surfaces with modified orthogonal frame, AIMS Mathematics, 5 (3), 2027-2039, 2020.
  • [5] Kelleci, A., Eren, K., On evolution of some associated type ruled surfaces, Mathematical Sciences and Applications E-Notes, 8 (2), 178-186, 2020.
  • [6] Hasimoto, H., Motion of a vortex filament and its relation to elastica, Journal of the Physical Society of Japan, 31, 293-294, 1971.
  • [7] Hasimoto, H., A soliton on a vortex filament, Journal of Fluid Mechanics, 51 (3), 477-485, 1972.
  • [8] Rogers, C., Schief, W.K., Bäcklund and Darboux transformations, Cambridge University Press, 432, 2002.
  • [9] Abdel-All, N.H., Hussien, R.A., Youssef, T., Hasimoto surfaces, Life Science Journal, 9 (3), 556-560, 2012.
  • [10] Kelleci, A., Bektaş, M., Ergüt, M., The Hasimoto surface according to Bishop frame, Adıyaman University Journal of Science, 9 (1), 13-22, 2019.
  • [11] Erdoğdu, M., Özdemir, M., Geometry of Hasimoto surfaces in Minkowski 3-space, Mathematical Physics, Analysis and Geometry, 17, 169-181, 2014.
  • [12] Çakmak, A., Öklid 3-uzayında Hasimoto yüzeylerinin paralel yüzeyleri, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 7 (1), 125-132, 2018.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Kemal Eren 0000-0001-5273-7897

Alev Kelleci Akbay 0000-0003-2528-2131

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 3 Kasım 2020
Kabul Tarihi 30 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 11 Sayı: 1

Kaynak Göster

APA Eren, K., & Kelleci Akbay, A. (2021). On the Harmonic Evolute Surfaces of Hasimoto Surfaces. Adıyaman University Journal of Science, 11(1), 87-100. https://doi.org/10.37094/adyujsci.820698
AMA Eren K, Kelleci Akbay A. On the Harmonic Evolute Surfaces of Hasimoto Surfaces. ADYU J SCI. Haziran 2021;11(1):87-100. doi:10.37094/adyujsci.820698
Chicago Eren, Kemal, ve Alev Kelleci Akbay. “On the Harmonic Evolute Surfaces of Hasimoto Surfaces”. Adıyaman University Journal of Science 11, sy. 1 (Haziran 2021): 87-100. https://doi.org/10.37094/adyujsci.820698.
EndNote Eren K, Kelleci Akbay A (01 Haziran 2021) On the Harmonic Evolute Surfaces of Hasimoto Surfaces. Adıyaman University Journal of Science 11 1 87–100.
IEEE K. Eren ve A. Kelleci Akbay, “On the Harmonic Evolute Surfaces of Hasimoto Surfaces”, ADYU J SCI, c. 11, sy. 1, ss. 87–100, 2021, doi: 10.37094/adyujsci.820698.
ISNAD Eren, Kemal - Kelleci Akbay, Alev. “On the Harmonic Evolute Surfaces of Hasimoto Surfaces”. Adıyaman University Journal of Science 11/1 (Haziran 2021), 87-100. https://doi.org/10.37094/adyujsci.820698.
JAMA Eren K, Kelleci Akbay A. On the Harmonic Evolute Surfaces of Hasimoto Surfaces. ADYU J SCI. 2021;11:87–100.
MLA Eren, Kemal ve Alev Kelleci Akbay. “On the Harmonic Evolute Surfaces of Hasimoto Surfaces”. Adıyaman University Journal of Science, c. 11, sy. 1, 2021, ss. 87-100, doi:10.37094/adyujsci.820698.
Vancouver Eren K, Kelleci Akbay A. On the Harmonic Evolute Surfaces of Hasimoto Surfaces. ADYU J SCI. 2021;11(1):87-100.

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https://doi.org/10.3934/math.2022985
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