• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1055-1059
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• 1996

We characterize the left invariant Riemannian metrics on SO(1,2) which give rise to 3- or 4-dimensional isometry groups.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.15-30
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• 2024

In this paper, we focus on partial isometry elements and strongly EP elements on a ring. We construct characterizing equations such that an element which is both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have a solution in a given set. In particular, an element a ∈ R^# ∩ R^† is a partial isometry element if and only if the equation x = x(a^†)^*a^† has at least one solution in {a, a#, a^†, a^*, (a^#)^*, (a^†)^*}. An element a ∈ R^#∩R^† is a strongly EP element if and only if the equation (a^†)^*xa^† = xa^†a has at least one solution in {a, a^#, a^†, a^*, (a^#)^*, (a^†)^*}. These characterizations extend many well-known results.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.425-444
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• 2013

We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane re ections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.971-986
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• 2001

Equations. See Full-text.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.351-360
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• 2022

We prove that a punctured-torus group of hyperbolic 4-space which keeps an embedded hyperbolic 2-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.

• Journal of the Korea Computer Graphics Society
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• v.3 no.2
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• pp.55-63
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• 1997

This paper presents a method of detecting motion isometry from the motions of two objects in a three-dimensional space. We define the motion isometry based on the group theory and a newly defined coordinate system. Motion isometry can be detected using the coordinate system which we call Motion Specific Coordinate System(MSCS). In addition, we present an algorithm if two motions are isometric using the coordinate system. The algorithm can detect the difference in the motions of objects irrespective of their positions or the directions of their motions in a space. The algorithm can also detect the motion difference in the case of segmented objects which have several joints. The motion quantity is represented by translation values or rotation angles about some axes.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.999-1006
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• 2015

In this paper, we deal with a characterization of the posets with the property that every poset isometry of $\mathbb{F}^n_q$ fixing the origin is a linear map. We say such a poset to be admitting the linearity of isometries. We show that a poset P admits the linearity of isometries over $\mathbb{F}^n_q$ if and only if P is a disjoint sum of chains of cardinality 2 or 1 when q = 2, or P is an anti-chain otherwise.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.725-735
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• 2016

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. There is a geometric condition equivalent to the rolling constraint which enables us to generalize the rolling motions for any two-dimensional Riemannian manifolds. This system has a five-dimensional phase space. In order to study the controllability of the rolling surfaces, we lift the system to a six-dimensional space and show that the lifted system is controllable unless the two surfaces have isometric universal covering spaces. In the non-controllable case there are some three-dimensional orbits each of which corresponds to an isometry of the universal covering spaces.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.783-796
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• 1994

Let V be a vector space of dimension m over Q, and let (, ) be a non-degenerate bilinear form on V. Let r be the Witt index of V, and let $V = V' + V_0 + V"$ be the Witt decomposition, where $V_0$ is anisotropic and V', V" are paired non-singularly. Let H = O(m-r, r) be the isometry group of V, (, ), viewed as an algebraic group over Q. Let G = Sp(n) be the symplectic group of rank n defined over Q.ed over Q.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.1-20
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• 2003

본 요약논문에서는 단순 연결된 리만곡면들의 isometry군, 그 군의 이산부분군을 이용한 리 만곡면들의 tessellation 그리고 regular map에 대해 소개하고 그 응용과 상호연관성들에 대해 살펴본다. 그리고, 여러가지 관점에서의 regular map의 분류에 대해 소개하고, 최근까지 연구되어진 바에 대해 정리해 보고자 한다.