Research Article
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Year 2021, Volume: 9 Issue: 1, 193 - 200, 28.04.2021

Abstract

References

  • [1] Aminov, Yu. Surfaces in E⁴ with a Gaussian Curvature Coinciding with a Gaussian Torsion up to the Sign, Math. Notes, 56(1994), 1211--1215.
  • [2]Arslan, K., Bayram, B., Bulca, B. and Öztürk, G. On Translation Surfaces in 4-dimensional Euclidean Space, Acta et Comm. Univ. Tartuensis Math., 20(2) (2016), 123-133.
  • [3]Aydın, M.E., Öğrenmiş, A.O. and Ergüt, M. Classification of factorable surfaces in the pseudo-Galilean 3-space, Glasnik Matematicki, 50(70)(2015), 441-451.
  • [4]Baba-Hamed, C., Bekkar, M. and Zoubir, H. Translation surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying Δr_{i}=λ_{i}r_{i}, Int. J. Math. Analysis, 4(17)(2010), 797-808.
  • [5]Bekkar, M. and Senoussi, B. Factorable surfaces in 3-dimensional Euclidean and Lorentzian spaces satisfying Δr_{i}=λ_{i}r_{i}, Int. J. Geom., 103(2012),17-29.
  • [6]Bulca, B. and Arslan, K. Surfaces given with the Monge patch in E⁴, Journal of Mathematical Physics, Analysis, Geometry, 9(4)(2013), 435--447.
  • [7]Büyükkütük, S. A Characterization of Factorable Surfaces, PhD. Thesis, Kocaeli University, 2018.
  • [8]Büyükkütük, S. A Characterization of Translation Surfaces in Euclidean Spaces, Master Thesis, Kocaeli University, 2012.
  • [9] Büyükkütük, S. Timelike Factorable Surfaces in Minkowski Space-Time, Sakarya Uni. J Sci., 22(6)(2018), 1939-1946.
  • [10] Büyükkütük, S. and Öztürk, G. A Characterization of Factorable Surfaces in Euclidean 4-space E⁴, Koc. J. Sci. Eng., 1(1)(2018), 15-20.
  • [11] Büyükkütük, S. and Öztürk, G. Spacelike Factorable Surfaces in Four Dimensional Minkowski Space, Bull. Math. An. App., 9(4)(2017), 12-20.
  • [12] Chen,B. Y., Geometry of Submanifolds, Dekker, New York(1973).
  • [13] Difi, S.A., Ali, H. and Zoubir, H. Translation-Factorable Surfaces in the 3-dimensional Euclidean and Lorentzian Spaces Satisfying Δr_{i}=λ_{i}r_{i}, EJMAA, 6(2)(2018), 227-236.
  • [14] Liu, H. Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom., 64(1999), 141-149.
  • [15] Liu, H. Translation surfaces with dependent Gaussian and mean curvature in 3-dimensional spaces, J. Northeast Univ. Tech., 14(1)(1993), 88-93.
  • [16] Lopez, R. and Moruz, M. Translation and homothetical surfaces in Euclidean spaces with constant curvature, J. Korean Math. Soc., 52(2015), 523-535.
  • [17] Lopez, R. Minimal translation surfaces in hyperbolic space, Beitrage Algebra Geom., 52(1)(2011), 105-112.
  • [18] Meng, H. and Liu, H. Factorable Surfaces in 3-Minkowski Space, Bull. Korean Math. Soc., 46(1)(2009), 155-169.
  • [19] Munteanu, M. and Nistor, A.I. On the geometry of the second fundamental form of translation surfaces in E³, Houston J. Math., 37(2011), 1087-1102.
  • [20] Senoussi, B., Bekkar, M. Translation and homothetical TH- surfaces in the 3-dimensional Euclidean space E³ and Lorentzian-Minkowski space E₁³ Open J. Math. Sci., 3(2019), 234-244.
  • [21] Verstraelen, L., Walrave, J. and Yaprak, Ş. The minimal translation surface in Euclidean space, Soochow J. Math., 20(1994), 77-82.
  • [22] Yu, Y. and Liu, H. The Factorable Minimal Surfaces, Proc. 11. Int. Workshop on Dif. Geom., 11(2007), 33-39.

Translation-Factorable Surfaces in 4-dimensional Euclidean Space

Year 2021, Volume: 9 Issue: 1, 193 - 200, 28.04.2021

Abstract

In this study we consider translation-factorable (TF-type) surfaces in Euclidean 4-space $\mathbb{E}^{4}$. We have calculated the Gaussian and mean curvature of the TF-type surfaces. Further, we give some sufficient conditions to become flat or minimal for these surfaces. Finally, we give some examples of TF-type surfaces and plot the projection of the graphics into the Euclidean 3-space.

References

  • [1] Aminov, Yu. Surfaces in E⁴ with a Gaussian Curvature Coinciding with a Gaussian Torsion up to the Sign, Math. Notes, 56(1994), 1211--1215.
  • [2]Arslan, K., Bayram, B., Bulca, B. and Öztürk, G. On Translation Surfaces in 4-dimensional Euclidean Space, Acta et Comm. Univ. Tartuensis Math., 20(2) (2016), 123-133.
  • [3]Aydın, M.E., Öğrenmiş, A.O. and Ergüt, M. Classification of factorable surfaces in the pseudo-Galilean 3-space, Glasnik Matematicki, 50(70)(2015), 441-451.
  • [4]Baba-Hamed, C., Bekkar, M. and Zoubir, H. Translation surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying Δr_{i}=λ_{i}r_{i}, Int. J. Math. Analysis, 4(17)(2010), 797-808.
  • [5]Bekkar, M. and Senoussi, B. Factorable surfaces in 3-dimensional Euclidean and Lorentzian spaces satisfying Δr_{i}=λ_{i}r_{i}, Int. J. Geom., 103(2012),17-29.
  • [6]Bulca, B. and Arslan, K. Surfaces given with the Monge patch in E⁴, Journal of Mathematical Physics, Analysis, Geometry, 9(4)(2013), 435--447.
  • [7]Büyükkütük, S. A Characterization of Factorable Surfaces, PhD. Thesis, Kocaeli University, 2018.
  • [8]Büyükkütük, S. A Characterization of Translation Surfaces in Euclidean Spaces, Master Thesis, Kocaeli University, 2012.
  • [9] Büyükkütük, S. Timelike Factorable Surfaces in Minkowski Space-Time, Sakarya Uni. J Sci., 22(6)(2018), 1939-1946.
  • [10] Büyükkütük, S. and Öztürk, G. A Characterization of Factorable Surfaces in Euclidean 4-space E⁴, Koc. J. Sci. Eng., 1(1)(2018), 15-20.
  • [11] Büyükkütük, S. and Öztürk, G. Spacelike Factorable Surfaces in Four Dimensional Minkowski Space, Bull. Math. An. App., 9(4)(2017), 12-20.
  • [12] Chen,B. Y., Geometry of Submanifolds, Dekker, New York(1973).
  • [13] Difi, S.A., Ali, H. and Zoubir, H. Translation-Factorable Surfaces in the 3-dimensional Euclidean and Lorentzian Spaces Satisfying Δr_{i}=λ_{i}r_{i}, EJMAA, 6(2)(2018), 227-236.
  • [14] Liu, H. Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom., 64(1999), 141-149.
  • [15] Liu, H. Translation surfaces with dependent Gaussian and mean curvature in 3-dimensional spaces, J. Northeast Univ. Tech., 14(1)(1993), 88-93.
  • [16] Lopez, R. and Moruz, M. Translation and homothetical surfaces in Euclidean spaces with constant curvature, J. Korean Math. Soc., 52(2015), 523-535.
  • [17] Lopez, R. Minimal translation surfaces in hyperbolic space, Beitrage Algebra Geom., 52(1)(2011), 105-112.
  • [18] Meng, H. and Liu, H. Factorable Surfaces in 3-Minkowski Space, Bull. Korean Math. Soc., 46(1)(2009), 155-169.
  • [19] Munteanu, M. and Nistor, A.I. On the geometry of the second fundamental form of translation surfaces in E³, Houston J. Math., 37(2011), 1087-1102.
  • [20] Senoussi, B., Bekkar, M. Translation and homothetical TH- surfaces in the 3-dimensional Euclidean space E³ and Lorentzian-Minkowski space E₁³ Open J. Math. Sci., 3(2019), 234-244.
  • [21] Verstraelen, L., Walrave, J. and Yaprak, Ş. The minimal translation surface in Euclidean space, Soochow J. Math., 20(1994), 77-82.
  • [22] Yu, Y. and Liu, H. The Factorable Minimal Surfaces, Proc. 11. Int. Workshop on Dif. Geom., 11(2007), 33-39.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Emine Pamuk This is me 0000-0001-9723-3983

Betül Bulca

Publication Date April 28, 2021
Submission Date February 5, 2020
Acceptance Date February 11, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Pamuk, E., & Bulca, B. (2021). Translation-Factorable Surfaces in 4-dimensional Euclidean Space. Konuralp Journal of Mathematics, 9(1), 193-200.
AMA Pamuk E, Bulca B. Translation-Factorable Surfaces in 4-dimensional Euclidean Space. Konuralp J. Math. April 2021;9(1):193-200.
Chicago Pamuk, Emine, and Betül Bulca. “Translation-Factorable Surfaces in 4-Dimensional Euclidean Space”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 193-200.
EndNote Pamuk E, Bulca B (April 1, 2021) Translation-Factorable Surfaces in 4-dimensional Euclidean Space. Konuralp Journal of Mathematics 9 1 193–200.
IEEE E. Pamuk and B. Bulca, “Translation-Factorable Surfaces in 4-dimensional Euclidean Space”, Konuralp J. Math., vol. 9, no. 1, pp. 193–200, 2021.
ISNAD Pamuk, Emine - Bulca, Betül. “Translation-Factorable Surfaces in 4-Dimensional Euclidean Space”. Konuralp Journal of Mathematics 9/1 (April 2021), 193-200.
JAMA Pamuk E, Bulca B. Translation-Factorable Surfaces in 4-dimensional Euclidean Space. Konuralp J. Math. 2021;9:193–200.
MLA Pamuk, Emine and Betül Bulca. “Translation-Factorable Surfaces in 4-Dimensional Euclidean Space”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 193-00.
Vancouver Pamuk E, Bulca B. Translation-Factorable Surfaces in 4-dimensional Euclidean Space. Konuralp J. Math. 2021;9(1):193-200.
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