• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.533-540
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• 2000

In the present paper, we study a non-degenrate ruled surface along a null curve in a 3-dimensional Minkowski space E31, which is called a null scroll, an investigate some characterizations of null scrolls satisfying the condition H=AH, A Mat(3, ), where denotes the Laplacian of the surface with respect to the induced metric, H the mean curvature vector and Mat(3, ) the set of 3$\times$3-real matrices.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.383-391
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• 1997

The main purpose of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Berwald type (a Berwald h-recurrent connection and a $F\Gamma$' connection) of a Finsler space and to seek the necessary and sufficient conditions that the induced connections coincide with the intrinsic connections. And we show the quantities and relations with respect to the respective induced connections. Finally we show some examples.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.917-931
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• 2013

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1421-1431
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• 2021

In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C⁰-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.379-396
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• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.557-573
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• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).

• East Asian mathematical journal
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• v.34 no.5
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.481-506
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• 2022

This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

• East Asian mathematical journal
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• v.33 no.5
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• pp.571-585
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• 2017

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigen vectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we showed that a 2-type surface M in $E^3$ satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle},{\rangle}$ is the usual inner product in $E^3$, then M is an open part of a circular cylinder. Also we showed that if a quadric hypersurface M in a Euclidean space satisfies ${\langle}{\Delta}x,x{\rangle}=c$ for a constant c, then it is one of a minimal quadric hypersurface, a genaralized cone, a hypersphere, and a spherical cylinder.