• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.273-293
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• 2016

In this paper, we obtain that every biharmonic non-degenerate hypersurfaces in semi-Euclidean space $E^5_s$ with constant scalar curvature of diagonal shape operator has zero mean curvature.

• 대한수학회논문집
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• 제37권3호
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• pp.865-879
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• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• 대한수학회논문집
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• 제38권4호
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.269-276
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• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• 호남수학학술지
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• 제33권1호
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• pp.121-127
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• 2011

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times $M = (a,\infty){\times}_fN$ with prescribed scalar curvature functions.

• 호남수학학술지
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• 제32권1호
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• pp.85-89
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• 2010

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times M = $({\alpha},{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• 호남수학학술지
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• 제33권4호
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• pp.487-493
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• 2011

The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, we define the parameter space of the t-manifold using its Fisher's matrix and characterize the t-manifold from the viewpoint of information geometry. The ${\alpha}$-scalar curvatures to the t-manifold are calculated.

• 호남수학학술지
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• 제31권3호
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• pp.381-398
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• 2009

Let $G\;=\;O(k){\times}O(k){\times}O(q)$ and let $M^n$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^{n+1}$. Then we obtain a theorem: If $M^n$ has 2 distinct principal curvatures at some point p, then the square norm of the second fundamental form of $M^n$, S = n.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.115-122
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• 1998

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on $M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$ with specific scalar curvatures.