scholarly journals Polynomial affine translation surfaces in Euclidean 3-space

2017 ◽  
Vol 37 (3) ◽  
pp. 195
Author(s):  
Hülya Gün Bozok ◽  
Mahmut Ergüt
Keyword(s):  
Constant Curvature ◽  
Existence Results ◽  
Translation Surfaces ◽  
Affine Translation

In this paper we study the polynomial affine translation surfaces in E3with constant curvature. We derive some non-existence results for suchsurfaces. Several examples are also given by figures.

Weingarten Affine Translation Surfaces in Euclidean 3-Space

2017 ◽  
Vol 72 (4) ◽  
pp. 1839-1848 ◽  
Author(s):  
Seoung Dal Jung ◽  
Huili Liu ◽  
Yixuan Liu
Keyword(s):  
Translation Surfaces ◽  
Affine Translation

Affine Translation Surfaces

1999 ◽  
Vol 35 (1-2) ◽  
pp. 134-144 ◽  
Author(s):  
M. Magid ◽  
L. Vrancken
Keyword(s):  
Translation Surfaces ◽  
Affine Translation

scholarly journals Classifications of translation surfaces in isotropic geometry with constant curvature

2020 ◽  
Vol 72 (3) ◽  
pp. 291-306
Author(s):  
M. E. Aydin
Keyword(s):  
Constant Curvature ◽  
Arbitrary Constant ◽  
Translation Surfaces

UDC 515.12 We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures underthe condition that at least one of translating curves lies in a plane.

scholarly journals Classification of j-maximal spacelike affine translation surfaces in the Minkovski space i31 with density

2019 ◽  
Vol 15 (3) ◽  
pp. 36
Author(s):  
Tran Le Nam
Keyword(s):  
Minkowski Space ◽  
Translation Surface ◽  
Maximal Surface ◽  
Translation Surfaces ◽  
Bernstein Theorem ◽  
Lagrange’S Equation ◽  
Affine Translation ◽  
Two Parameters

An affine translation surface is a graph of a function   introduced by Liu and Yu in 2013. The article considers the spacelike affine translation surfaces in the Minkowski space  with density  establishing the Lagrange’s equation type for -maximal surface, classifying -maximal spacelike affine translation surfaces. The result obtains two parameters and . From that, the Calabi – Bernstein theorem in this space is not true because two function  and  are defined on  

Affine translation surfaces with constant sectional curvature

2000 ◽  
Vol 68 (1-2) ◽  
pp. 192-199 ◽  
Author(s):  
Martin Magid ◽  
Luc Vrancken
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Translation Surfaces ◽  
Affine Translation
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