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Yıl 2023, , 25 - 32, 22.03.2023
https://doi.org/10.17798/bitlisfen.1170647

Öz

Kaynakça

  • [1] B. Bulca, K. Arslan, " Surfaces Given with the Monge Patch in E^4 ," Journal of Mathematical Physics, Analysis, Geometry, vol. 9, pp. 435-447, 2013.
  • [2] S. Büyükkütük, G. Öztürk, "A new type timelike surface given with Monge patch in E^4 , " TWMS J. App. and Eng. Math., vol. 11, 176–183, 2021.
  • [3] B.Y. Chen, Geometry of Submanifolds. New York: Dekker, 1973.
  • [4] B.Y. Chen, M. Choi, Y.H. Kim, "Surfaces of revolution with pointwise 1-type Gauss map.," J. Korean Math. Soc. vol . 42, 447–455, 2005.
  • [5] G. Gray, "A Monge Patch.," Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton. FL: CRC Press. pp. 398–401, 1997.
  • [6] J. Glymph, D. Schelden, C. Ceccato, J.Mussel, H. Schober, "A parametric strategy for free-form glass structures using quadrilateral planar facets," Automation in Construction, vol. 13, 187–202, 2004.
  • [7] E.A. Pamuk, B. Bulca, "Translation-Factorable Surfaces in 4-dimensional Euclidean Space," Konuralp Journal of Mathematics. Vol. 9, 193–200, 2021.
  • [8] L. Verstraelen, J. Walrave, S. Yaprak, "The Minimal Translation Surface in Euclidean Space," Schoow J. Math., vol. 20, 77–82, 1994.

A new characterization of Aminov surface with regards to its Gauss map in E^4

Yıl 2023, , 25 - 32, 22.03.2023
https://doi.org/10.17798/bitlisfen.1170647

Öz

In this work, we focus on Aminov surface with regard to its Gauss map in E^4. Firstly, we write the covariant derivatives according to linear combinations of orthonormal vectors and separate the equalities using Gauss and Weingarten formulas. Then, we get the laplace of the Gauss map. After giving some conditions, we yield as main results: Aminov surfaces can not have harmonic Gauss map and can not have pointwise one-type Gauss map of I. kind in E^4. Further, we give an example of helical cylinder which is also congruent to an Aminov surface. Lastly, we obtain the conditions of having pointwise one-type Gauss map of II. kind.

Kaynakça

  • [1] B. Bulca, K. Arslan, " Surfaces Given with the Monge Patch in E^4 ," Journal of Mathematical Physics, Analysis, Geometry, vol. 9, pp. 435-447, 2013.
  • [2] S. Büyükkütük, G. Öztürk, "A new type timelike surface given with Monge patch in E^4 , " TWMS J. App. and Eng. Math., vol. 11, 176–183, 2021.
  • [3] B.Y. Chen, Geometry of Submanifolds. New York: Dekker, 1973.
  • [4] B.Y. Chen, M. Choi, Y.H. Kim, "Surfaces of revolution with pointwise 1-type Gauss map.," J. Korean Math. Soc. vol . 42, 447–455, 2005.
  • [5] G. Gray, "A Monge Patch.," Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton. FL: CRC Press. pp. 398–401, 1997.
  • [6] J. Glymph, D. Schelden, C. Ceccato, J.Mussel, H. Schober, "A parametric strategy for free-form glass structures using quadrilateral planar facets," Automation in Construction, vol. 13, 187–202, 2004.
  • [7] E.A. Pamuk, B. Bulca, "Translation-Factorable Surfaces in 4-dimensional Euclidean Space," Konuralp Journal of Mathematics. Vol. 9, 193–200, 2021.
  • [8] L. Verstraelen, J. Walrave, S. Yaprak, "The Minimal Translation Surface in Euclidean Space," Schoow J. Math., vol. 20, 77–82, 1994.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Sezgin Büyükkütük 0000-0002-1845-0822

Günay Öztürk 0000-0002-1608-0354

Yayımlanma Tarihi 22 Mart 2023
Gönderilme Tarihi 6 Ekim 2022
Kabul Tarihi 20 Mart 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

IEEE S. Büyükkütük ve G. Öztürk, “A new characterization of Aminov surface with regards to its Gauss map in E^4”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 12, sy. 1, ss. 25–32, 2023, doi: 10.17798/bitlisfen.1170647.



Bitlis Eren Üniversitesi
Fen Bilimleri Dergisi Editörlüğü

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