Research Article

Translation surfaces in affine 3-space

Volume: 49 Number: 6 December 8, 2020
EN

Translation surfaces in affine 3-space

Abstract

In this paper, we study translation surfaces in three dimensional affine space. We characterize the finite type non-degenerate translation surfaces with respect to the first affine and the second affine fundamental forms.

Keywords

References

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  3. [3] K. Arslan, B. Bayram, B. Bulca and G. Ozturk, On translation surfaces in 4- dimensional Euclidean space, Acta Comment. Univ. Tartu. Math. 20 (2), 123–133, 2016.
  4. [4] M. Bekkar and B. Senoussi, Translation surfaces in the 3-dimensional space satisfying $\Delta^{III}r_i=\mu_i r_i$, J. Geom. 103 (3), 367-374, 2012.
  5. [5] W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, Berlin, 1923.
  6. [6] Ch. Baba-Hamed, M.Bekkar and H. Zoubir, Translation surfaces in the threedimensional Lorentz-Minkowski space satisfying $\Delta r_{i}=\lambda _{i}r_{i},$, Int. J. Math. Anal. 4 (17), 797–808, 2010.
  7. [7] B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore, 1984.
  8. [8] F. Dillen, J. Pas and L. Vertraelen, On surfaces of finite type in Euclidean 3-space, Kodai Math. J. 13 (1), 10-21, 1990.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

December 8, 2020

Submission Date

May 14, 2019

Acceptance Date

February 27, 2020

Published in Issue

Year 2020 Volume: 49 Number: 6

APA
Lone, M. S., Karacan, M. K., Tunçer, Y., & Es, H. (2020). Translation surfaces in affine 3-space. Hacettepe Journal of Mathematics and Statistics, 49(6), 1944-1954. https://doi.org/10.15672/hujms.564921
AMA
1.Lone MS, Karacan MK, Tunçer Y, Es H. Translation surfaces in affine 3-space. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):1944-1954. doi:10.15672/hujms.564921
Chicago
Lone, Moahmd Saleem, Murat Kemal Karacan, Yilmaz Tunçer, and Hasan Es. 2020. “Translation Surfaces in Affine 3-Space”. Hacettepe Journal of Mathematics and Statistics 49 (6): 1944-54. https://doi.org/10.15672/hujms.564921.
EndNote
Lone MS, Karacan MK, Tunçer Y, Es H (December 1, 2020) Translation surfaces in affine 3-space. Hacettepe Journal of Mathematics and Statistics 49 6 1944–1954.
IEEE
[1]M. S. Lone, M. K. Karacan, Y. Tunçer, and H. Es, “Translation surfaces in affine 3-space”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, pp. 1944–1954, Dec. 2020, doi: 10.15672/hujms.564921.
ISNAD
Lone, Moahmd Saleem - Karacan, Murat Kemal - Tunçer, Yilmaz - Es, Hasan. “Translation Surfaces in Affine 3-Space”. Hacettepe Journal of Mathematics and Statistics 49/6 (December 1, 2020): 1944-1954. https://doi.org/10.15672/hujms.564921.
JAMA
1.Lone MS, Karacan MK, Tunçer Y, Es H. Translation surfaces in affine 3-space. Hacettepe Journal of Mathematics and Statistics. 2020;49:1944–1954.
MLA
Lone, Moahmd Saleem, et al. “Translation Surfaces in Affine 3-Space”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 6, Dec. 2020, pp. 1944-5, doi:10.15672/hujms.564921.
Vancouver
1.Moahmd Saleem Lone, Murat Kemal Karacan, Yilmaz Tunçer, Hasan Es. Translation surfaces in affine 3-space. Hacettepe Journal of Mathematics and Statistics. 2020 Dec. 1;49(6):1944-5. doi:10.15672/hujms.564921

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