Translation surfaces in affine 3-space

References (19)

1. M. Andrade, Calculus of affine structures and applications for isosurfaces (in portuguese), PhD dissertation, Rio de Janeiro, August, 2011
2. M. Andrade and T. Lewiner, Affine-invariant curvature estimators for implicit surfaces, Comput. Aided Geom. Des. 29, 162–173, 2012
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. 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. W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, Berlin, 1923
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. B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore, 1984
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
9. O.J. Garay, An extension of Takahashis theorem, Geom. Dedicata, 34 (2), 105-112, 1990
10. W. Goemans, Surfaces in three-dimensional Euclidean and Minkowski space, in particular a study of Weingarten surfaces, PhD. Dissertation, September, 2010
11. E.F.C. Huamani, Affine Minimal surfaces with singularities, Masters dissertation, Rio de Janeiro, September, 2017
12. Y. Fu and Z.H. Hou, Affine translation surfaces with constant Gauss curvatures, Kyungpook Math. J. 50, 337–343, 2010
13. M.K. Karacan, D.W. Yoon and B. Bukcu, Translation surfaces in the three dimensional simply isotropic space $\mathbb{I}_3^1$, Int. J. Geom. Methods Mod. Phys. 13 (7), 1650088, 9 pp., 2016
14. A.M. Li, U. Simon and G. Zhao, Global affine differential geometry of hypersurfaces, De Gruyter Expositions Math., 328 pages, 1993
15. M. Magid and L.Vrancken, Affine translation surfaces, Results Math. 35, 134–144, 1999
16. F. Manhart, Die AffinminimalrückungsflÄchen, Arch. Math. 44, 547–556, 1985
17. U. Simon, A. Schwenk-Schellschmidt and H. Viesel, Introduction to the affine differential geometry of hypersurfaces. Lecture Notes, Science Univ. Tokyo Press, 1991
18. H. Sun, On affine translation surfaces of constant mean curvature, Kumamoto J. Math. 13, 49–57, 2000
19. Y. Yang, Y.H. Yu and H.L. Liu, Linear Weingarten centroaffine translation surfaces in $\mathbb{R}^3$, J. Ma