• 대한수학회지
• /
• 제36권3호
• /
• pp.621-631
• /
• 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.

• 호남수학학술지
• /
• 제29권3호
• /
• pp.481-493
• /
• 2007

We will construct several types of semi-regular tilings of a hyperbolic unit disk model by defining geometric features of the definition of distance in a hyperbolic plane, area of triangle, and isometry of inversions. We researched the method of regular tilings and semi-regular tilings of hyperbolic unit disk model and wrote an semi-regular tiling construction algorithm using Cabri2 program and Cinderella program. Lastly, We want to make a product related to traditional heritage cultural patterns using Photoshop, so we'll model the advertising photos of cites; Seoul, Gwangju.

• 정보처리학회논문지A
• /
• 제8A권4호
• /
• pp.489-498
• /
• 2001

본 논문에서는 하이퍼볼릭 평면에서 임의의 분산 데이터 보간을 지역적으로 제어하는 새로운 방법을 개발하였다. 지역적 제어와 관련된 주제는 상호대화형식의 디자인분야에서 매우 중요하다. 특히 본 논문에서 제안한 방법은 하이퍼볼릭 평면상에서 형성되는 genus-N 객체 모델을 상호대화형식으로 디자인하는데 유효하게 적용될 수 있다. 특 변화된 데이터가 미치는 영향이 일정한 지역에만 국한되므로 일반 사용자가 genus-N객체를 상호대화형으로 디자인하기가 훨씬 편리하다. 따라서, 본 연구은 genus-N 객체를 형성하는데 사용한 하이퍼볼릭 평면상에서의 전역적 보간법을 발전시켜 하이퍼볼릭 평면에서의 지역적 보간법개발 및 구현을 목적으로 하고 있다. 이는 다음과 같은 주요 과정을 통하여 구현된다. 먼저, 보간 함수를 지역화하기 위하여 하이퍼볼릭 영역을 임의의 삼각형 패치로 세분화하고 각 데이터에 인접한 삼각형 패치들의 모임을 부 영역이라고 정의한다. 각 부 영역에서 가중치 함수가 설정된다. 마지막으로 중첩된 삼각형 영역의 세 개의 가중치를 혼합함으로써 지역적 보간 함수가 완성된다. 그 결과로서, 여러 개의 샘플 데이터 및 함수를 사용하여 전역적MQ 보간법과 비교한다.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.327-338
• /
• 2021

In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G^*₂(ℂ^m+2). Next, we show a non-existence property of real hypersurfaces in G^*₂(ℂ^m+2) satisfying such a curvature condition.

• 대한수학회보
• /
• 제60권2호
• /
• pp.507-514
• /
• 2023

Suppose that a line passing through a given point P intersects a given circle 𝓒 at Q and R in the Euclidean plane. It is well known that |PQ||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

• 대한수학회보
• /
• 제59권2호
• /
• pp.351-360
• /
• 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.

• Korean Journal of Mathematics
• /
• 제30권4호
• /
• pp.643-652
• /
• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• 충청수학회지
• /
• 제22권4호
• /
• pp.771-776
• /
• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• 호남수학학술지
• /
• 제22권1호
• /
• pp.83-90
• /
• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• 충청수학회지
• /
• 제20권3호
• /
• pp.203-210
• /
• 2007

Let X be a hyperbolic region in the complex plane C such that the hyperbolic metrix ${\lambda}_X(w){\mid}dw{\mid}$ exists. Let $R(X)=sup\{{\delta}_X(w):w{\in}X\}$ where ${\delta}_X(w)$ is the euclidean distance from w to ${\partial}X$. Here ${\partial}X$ is the boundary of X. A hyperbolic region X is called a Bloch region if R(X) < ${\infty}$. In this paper, we obtain lower bounds for the hyperbolic metric on Bloch regions in terms of the distance to the boundary.