• The Pure and Applied Mathematics
• /
• v.28 no.1
• /
• pp.43-53
• /
• 2021

We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.337-343
• /
• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• Honam Mathematical Journal
• /
• v.44 no.1
• /
• pp.36-51
• /
• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1329-1343
• /
• 2013

In this paper, we define translation surfaces in the 3-dimensional Heisenberg group $\mathcal{H}_3$ obtained as a product of two planar curves lying in planes, which are not orthogonal, and study minimal translation surfaces in $\mathcal{H}_3$.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.831-842
• /
• 2022

In this work we classified translation invariant surfaces with zero Gaussian curvature in the 3-dimensional Sol Lie group endowed with Lorentzian metric.

• Journal of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.523-535
• /
• 2015

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.249-266
• /
• 2024

In this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model ℋ³₁ of the anti-de Sitter space ℍ³₁ . We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of ℋ³₁.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1241-1254
• /
• 2017

In this paper, we classify translation surfaces in the three dimensional Galilean space ${\mathbb{G}}_3$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.953-965
• /
• 2017

In this paper, we classify translation surfaces of Type 2 in the three dimensional simply isotropic space ${\mathbb{I}}_3^1$ 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.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.959-972
• /
• 2021

In this paper, we define and classify minimal translation surfaces with respect to a kind of semi-symmetric metric connections and a kind of semi-symmetric non-metric connections in ℝ³ and ℝ³₁.