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 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.

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.

Translation surfaces in the three-dimensional simply isotropic space 𝕀31

2019 ◽  
Vol 16 (01) ◽  
pp. 1992001
Author(s):  
Murat Kemal Karacan ◽  
Dae Won Yoon ◽  
Bahaddin Bukcu
Keyword(s):  
Three Dimensional ◽  
Translation Surfaces ◽  
Isotropic Space ◽  
Simply Isotropic Space

In [M. K. Karacan, D. W. Yoon and B. Bukcu, Translation surfaces in the three-dimensional simply isotropic space [Formula: see text], Int. J. Geom. Methods Mod. Phys. 13(7) (2016) 1650088], there is a mistake in Theorem 5 that appeared in the paper. We here provide a correct theorem.

scholarly journals Constant mean curvature spheres in homogeneous three-manifolds

2020 ◽  
Author(s):  
William H. Meeks ◽  
Pablo Mira ◽  
Joaquín Pérez ◽  
Antonio Ros
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Complete Classification ◽  
Homogeneous Manifolds ◽  
The Mean

Abstract We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

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.

scholarly journals Weighted minimal translation surfaces in the Galilean space with density

2017 ◽  
Vol 15 (1) ◽  
pp. 459-466 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Mean Curvature ◽  
Linear Density ◽  
Translation Surface ◽  
Plane Curves ◽  
Isotropic Plane ◽  
Translation Surfaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Galilean Space ◽  
Log Linear

Abstract Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify such a surface with vanishing weighted mean curvature.

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  

Parabolic Revolution Surfaces of Finite Type in Simply Isotropic 3-spaces

2020 ◽  
pp. 2150034
Author(s):  
Alev Kelleci Akbay
Keyword(s):  
Finite Type ◽  
Laplace Operator ◽  
Fundamental Form ◽  
Three Dimensional ◽  
Second Fundamental Form ◽  
Real Numbers ◽  
Isotropic Space ◽  
Simply Isotropic Space ◽  
Revolution Surfaces ◽  
The Laplace Operator

In this paper, we classify parabolic revolution 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 first and second fundamental form and [Formula: see text], [Formula: see text] are some real numbers. Also, as an application, we give some explicit examples for these surfaces.

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