• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1169-1180
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• 1999

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.721-727
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• 2021

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1093-1102
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• 2007

In this note we survey some recent results on symmetric space, and related topics like rigidity, flexibility and geometry-topology aspect of symmetric space, specially in the line of hyperbolic 3-manifolds.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.375-385
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• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10b
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• pp.217-219
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• 2001

복잡한 제어가 필요한 설비의 운전 정보나 네트워크 연결 상태 또는 웹 문서간의 정보 등을 제한된 컴퓨터 화면에 효과적으로 배치하는 시각화 기법에 관한 논의가 활발히 진행되고 있다. 이 경우 한눈에 전체 정보의 계층 구조를 파악하도록 하는 환경을 제공하며, 사용자가 관심 있는 정보에 대해서는 전체 정보 계층 구조를 유지하면서 보다 상세히 그 내용을 보여주는 그래픽 기반의 사용자 인터페이스 판결의 개발이 필요하다. 이에 쌍곡선 기하학(Hyperbolic Geometry)을 기반으로 한 시각화기법으로 새로운 제어 환경을 구현하여 사용자의 편의를 도모하도록 한다.

• Journal of Korean Association for Spatial Structures
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• v.16 no.3
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• pp.67-78
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• 2016

Determining of the shape in the process of design for natural draught cooling tower is very important, because the shape of hyperbolic shell is respond sensitively to dynamic behavior of the whole cooling tower against wind load. In engineering practice, the geometric parameters have been determining based on the natural frequency. This study analyses influence of the tower shell geometric parameters on the structural behavior. For three representative models were selected, they were analyzed based on evaluation of damage by means of nonlinear FE-method. As a result, a hyperbolic rotational shell with the small radius overall was the lowest damage index induced by sufficient capacity of the stress redistribution and thus a wind-insensitive structure.

• 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 for History of Mathematics
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• v.13 no.2
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• pp.73-86
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• 2000

This paper introduces an hypermedia program supportable for teaching secondary and upper secondary level geometry. This program links users to files written in other softwares and internet web sites to provide information and exploratory environments with softwares. The linkage with the interactive dynamic software(GSP) files to teach hyperbolic geometry is illustrated with sample screens.