• East Asian mathematical journal
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• 제33권1호
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• pp.115-121
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• 2017

The purpose of this paper is to show how to represent a maximal spacelike surface in $L^n$ in terms of its generalized Guass map.

• 대한수학회지
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• 제48권5호
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• pp.1083-1100
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• 2011

We show that some class of spacelike maximal surfaces and timelike minimal surfaces match smoothly across the singular curve of the surfaces. Singular Bj$\"{o}$rling representation formulae for generalized spacelike maximal surfaces and for generalized timelike minimal surfaces play important roles in the explanation of this phenomenon.

• 대한수학회보
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• 제52권1호
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• East Asian mathematical journal
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• 제35권1호
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• pp.109-115
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• 2019

The purpose of this paper is to investigate various kinds of degeneracy of maximal surfaces in ${\mathbb{L}}^n$ in view of the generalized Gauss map.

• 충청수학회지
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• 제28권4호
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• pp.525-535
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• 2015

In this paper, we study on spinors with two hyperbolic components. Firstly, we express the hyperbolic spinor representation of a spacelike curve dened on an oriented (spacelike or time-like) surface in Minkowski space ${\mathbb{R}}^3_1$. Then, we obtain the relation between the hyperbolic spinor representation of the Frenet frame of the spacelike curve on oriented surface and Darboux frame of the surface on the same points. Finally, we give one example about these hyperbolic spinors.

• 호남수학학술지
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• 제38권1호
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• pp.151-167
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• 2016

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.

• 대한수학회보
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• 제51권6호
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• pp.1863-1874
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• 2014

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.

• East Asian mathematical journal
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• 제32권1호
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• pp.93-100
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• 2016

The generalized Gaussian image of a spacelike surface in $L^n$ lies in the indefinite positive quadric ${\mathbb{Q}}_+^{n-2}$ in the open submanifold ${\mathbb{C}}P_+^{n-1}$ of the complex projective space ${\mathbb{C}}P^{n-1}$. The purpose of this paper is to find out detailed information about ${\mathbb{Q}}_+^{n-2}{\subset}{\mathbb{C}}P_+^{n-1}$.

• 호남수학학술지
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• 제39권4호
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• pp.603-616
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• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

• 대한수학회보
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• 제52권2호
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• pp.377-394
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• 2015

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B$\ddot{a}$cklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B$\ddot{a}$cklund transformations on Razzaboni surfaces commute.