A generalization of translation surfaces with constant curvature in the isotropic space

2015 ◽  
Vol 107 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Muhittin Evren Aydin
Keyword(s):  
Constant Curvature ◽  
Translation Surfaces ◽  
Isotropic Space

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.

scholarly journals Constant curvature surfaces in a pseudo-isotropic space

2018 ◽  
Vol 49 (3) ◽  
pp. 221-233 ◽  
Author(s):  
Muhittin Evren Aydin
Keyword(s):  
Constant Curvature ◽  
Local Structure ◽  
Mean Curvature ◽  
Plane Curve ◽  
Surfaces Of Revolution ◽  
Curves And Surfaces ◽  
Isotropic Space ◽  
Constant Curvature Surfaces

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space $\mathbb{I}_{p}^{3}$ that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in $\mathbb{I}_{p}^{3}$ has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in $\mathbb{I}_{p}^{3}$. As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature.

Ruled surfaces generated by elliptic cylindrical curves in the isotropic space

2019 ◽  
Vol 26 (3) ◽  
pp. 331-340 ◽  
Author(s):  
Muhittin Evren Aydin ◽  
Adela Mihai
Keyword(s):  
Vector Field ◽  
Constant Curvature ◽  
Ruled Surfaces ◽  
Laplacian Operator ◽  
Position Vector ◽  
Isotropic Space

Abstract In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the isotropic 3-space {\mathbb{I}^{3}} . We classify such surfaces in {\mathbb{I}^{3}} with constant curvature and satisfying an equation in terms of the components of the position vector field and the Laplacian operator. Several examples are given and illustrated by figures.

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.

Translation surfaces in the three-dimensional simply isotropic space 𝕀31

2016 ◽  
Vol 13 (07) ◽  
pp. 1650088 ◽  
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Bahaddin Bukcu
Keyword(s):  
Real Number ◽  
Laplace Operator ◽  
Three Dimensional ◽  
Translation Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
The Laplace Operator

In this paper, we classify translation surfaces in the three-dimensional simply isotropic space [Formula: see text] under the condition [Formula: see text] where [Formula: see text] is the Laplace operator with respect to the first and second fundamental forms and [Formula: see text] is a real number. We also give explicit forms of these surfaces.

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

2018 ◽  
Vol 49 (1) ◽  
pp. 67-77
Author(s):  
Mohamd Saleem Lone ◽  
Murat Kemal Karacan
Keyword(s):  
Mean Curvature ◽  
Three Dimensional ◽  
Translation Surface ◽  
Translation Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
Dual Translation

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.

scholarly journals Constant Curvature Translation Surfaces in Galilean 3-Space

2019 ◽  
Vol 12 (1) ◽  
pp. 9-19
Author(s):  
Muhittin Evren AYDIN ◽  
Mihriban Alyamaç KÜLAHÇI ◽  
Alper Osman ÖĞRENMİŞ
Keyword(s):  
Constant Curvature ◽  
Translation Surfaces
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