scholarly journals Holomorphic representation of minimal surfaces in simply isotropic space

2021 ◽  
Vol 112 (3) ◽  
Author(s):  
Luiz C. B. da Silva
Keyword(s):  
Minimal Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
Holomorphic Representation

scholarly journals Classification of Some Special Types Ruled Surfaces in Simply Isotropic 3-Space

2017 ◽  
Vol 55 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Nural Yuksel
Keyword(s):  
Real Number ◽  
Laplace Operator ◽  
Fundamental Form ◽  
Three Dimensional ◽  
Ruled Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
The Laplace Operator ◽  
First Fundamental Form

AbstractIn this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I13under the condition ∆xi= λixiwhere ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.

scholarly journals Helicoidal Surfaces in the three dimensional simply isotropic space I₃¹

2017 ◽  
Vol 48 (2) ◽  
pp. 123-134
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Sezai Kiziltug
Keyword(s):  
Fundamental Form ◽  
Three Dimensional ◽  
Algebraic Equations ◽  
The Third ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
Helicoidal Surfaces ◽  
Coordinate Functions ◽  
Third Fundamental Form ◽  
Laplacian Operators

In this paper, we classify helicoidal surfaces in the three dimensional simply isotropic space  I₃¹ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.

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.

Some integral geometric results in the simply isotropic space

2003 ◽  
Vol 77 (1-2) ◽  
pp. 8-21
Author(s):  
Adrijan Borisov ◽  
Margarita Spirova
Keyword(s):  
Isotropic Space ◽  
Simply Isotropic Space

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.

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