• 대한수학회지
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• 제54권2호
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• pp.381-397
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• 2017

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies ${\square}G=f(G+C)$ for a smooth function f and a constant vector C, where ${\square}$ denotes the ChengYau operator. In particular, we obtain classification theorems on the rotational surfaces in ${\mathbb{E}}^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.167-177
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• 2022

In this manuscript, we handle a tubular surface whose Gauss map G satisfies the equality L₁G = f(G + C) for the Cheng-Yau operator L₁ in Galilean 3-space 𝔾₃. We give an example of a tubular surface having L₁-harmonic Gauss map. Moreover, we obtain a complete classification of tubular surface having L₁-pointwise 1-type Gauss map of the first kind in 𝔾₃ and we give some visualizations of this type surface.

• 대한수학회논문집
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• 제12권1호
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• pp.79-86
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• 1997

It is well-known that a null 2-type surface in 3-dimensional Euclidean space $E^#$ is an open portion of circular cylinder. In this article we prove that a surface with 2-type and 1-type Gauss map in $E^3$ is in fact of null 2-type and thus it is an open portion of circular cylinder.

• 대한수학회보
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• 제31권1호
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• pp.125-132
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• 1994

• 대한수학회지
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• 제53권6호
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• pp.1309-1330
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• 2016

As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.

• 대한수학회보
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• 제48권3호
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• pp.601-609
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• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

• 대한수학회논문집
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• 제18권2호
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• pp.289-295
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• 2003

In this paper, we study ruled surfaces in Minkowski space, which admit 1-type Gauss map. In particular, non-cylindrical ruled surfaces with finite type Gauss map are of k-type (k $\geq$ 2).

• 대한수학회보
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• 제46권3호
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• pp.567-576
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• 2009

We classify and characterize the rational helicoidal surfaces in a three-dimensional Minkowski space satisfying pointwise 1-type like problem on the Gauss map.

• 대한수학회보
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• 제50권3호
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.585-597
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• 2020

In this study, we classify surfaces of revolution of Type 1 in the three dimensional Galilean space 𝔾₃ in terms of the position vector field, Gauss map, and Laplacian operator of the first and the second fundamental forms on the surface. Furthermore, we give a classification of surfaces of revolution of Type 1 generated by a non-isotropic curve satisfying the pointwise 1-type Gauss map equation.