Dual translation surfaces in the three dimensional simply isotropic space $\mathbb{I}_{3}^{1}$

Mohamd Saleem Lone, Murat Kemal Karacan


In this paper, we study the dual translation surfaces in three dimensional simply isotropic space. We give classification of dual translation surface with constant dual isotropic mean curvature or constant dual isotropic Guassian curvature.


Dual surface, simply isotropic space, translation surface

Full Text:



M. E. Aydin, A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom., 107(2016), 603--615.

B. Bukcu, D. W. Yoon and M. K. Karacan, Translation surfaces in the 3-dimensional simply isotropic space $mathbb{I}_{3}^{1}$ satisfying $Delta ^{III}x_{i}=lambda _{i}x_{i}$, Konuralp Journal of Mathematics, 4(2016), 275-281.

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(2016), 1650088.

M. K. Karacan and N. Yuksel, Translation Surfaces of Type $3$ in the Three Dimensional Simply Isotropic Space, submitted.

M. K. Karacan, N. Yuksel, A. Cakmak and S. Kizltug, Dual Surfaces Defined by $z=f(u)+g(v)$ in Simply Isotropic $3$-Space,submitted.

H. Pottmann, P. Grohs and N. J. Mitra, Laguerre minimal surfaces, isotropic geometry and linear elasticity,Adv. Comput. Math., (2009),31:391.

H. Pottmann and Y. Liu, Discrete Surfaces in Isotropic Geometry, Mathematics of Surfaces XII,Volume 4647 of the series Lecture Notes in Computer Science, (2007), 341--363.

H. Sachs, Isotrope Geometrie des Raumes, Vieweg Verlag, Braunschweig, 1990.

Z. M. Sipus, Translation Surfaces of constant curvatures in a simply Isotropic space}, Period Math. Hung., 68(2014),160--175.

K. Strubecker, Differentialgeometrie des Isotropen raumes III, Flachentheorie, Math. Zeitsch., 48(1942),369--427.

K. Strubecker, Duale Minimalflachen des isotropen Raumes, Rad JAZU, 382(1978), 91--107.

D. W. Yoon and J. W. Lee, Linear Weingarten Helicoidal Surfaces in Isotropic Space, Symmetry 2016, 8, 126; doi:10.3390/sym8110126

DOI: http://dx.doi.org/10.5556/j.tkjm.49.2018.2476

Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) | Powered by MathJax