• 대한수학회보
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• 제51권4호
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• pp.957-964
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• 2014

In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($M_{\alpha},d_{\alpha}$)} of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_{\alpha}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($M_{\alpha},d_{\alpha}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.

• 한국게임학회 논문지
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• 제17권5호
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• pp.89-102
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• 2017

사회적으로 일상생활에서의 건강에 대한 관심이 높아짐에 따라 ICT기술을 스포츠에 적용시키려는 다양한 학문분야의 융합연구들이 진행되고 있다. 본 연구를 통해 지속적으로 균형을 유지해야 주행이 가능한 스마트 바이크를 개발하고, 이를 체험하기 위한 스튜디오 공간의 인터페이스를 설계하여 제안하고자 한다. 스튜디오는 체험을 위한 장치인 스마트 바이크와 1인용 콘텐츠의 몰입을 위한 지오데식 돔 스크린, 그리고 다양한 현실공간의 경치를 즐길 수 있도록 구현된 가상현실 콘텐츠로 구성되어져 있다. 스마트 바이크를 위한 1인용 체험공간에 최적화된 스튜디오의 설계 및 제작을 시도하였다는 점에서 의의가 있으며, 확장 가능성이 높은 인터페이스를 가지기 때문에 스포테인먼트를 위한 체험형 콘텐츠에 적용이 가능할 것으로 기대해 볼 수 있겠다.

• 대한수학회보
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• 제55권4호
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• 대한수학회지
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• 제58권6호
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.349-361
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• 2012

CAT(0) cubical complexes are a key to formulate geodesic spaces with nonpositive curvatures. The paper discusses the median structure of CAT90) cubical complexes. Especially, the underlying graph of a CAT(0) cubical complex is a median graph. Using the idea of median structure, this paper shows that groups acting on median complexes L(${\delta}$) groups and, in addition, work L(0) groups are closed under free product.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.513-535
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• 2017

As a continuation to the study in [8, 12, 15, 17], we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space ${\mathbb{E}}^3$. For such surfaces, local study is given and some examples are constructed using computer aided geometric design (CAGD).

• 대한수학회지
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• 제51권6호
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• pp.1105-1122
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• 2014

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, specific properties and existence of non-geodesic biharmonic curves for some classes of Finsler spaces. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

• 대한수학회보
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• 제31권1호
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• pp.25-33
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• 1994

In [2] we proved that if the minimum of the sectional curvature of a compact real minimal hypersurface of CP$^{m}$ is 1/(2m-1), then M is the geodesic hypersphere. This result was generalized in [8] to the case of M is a generic submanifold with flat normal connection. The purpose of the present paper is to prove a following generalization of theorems in [2] and [8].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.29-38
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• 2010

We study the geometry of half light like submanifold M of a semi-Riemannian space form $\bar{M}$(c) subject to the conditions : (a) the screen distribution on M is totally umbilic in M and the coscreen distribution on M is conformal Killing on $\bar{M}$ or (b) the screen distribution is totally geodesic in M and M is irrotational.