• 대한수학회지
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• 제55권2호
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• pp.415-424
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• 2018

General (${\alpha},\;{\beta}$)-metrics form a rich and important class of Finsler metrics. In this paper, we obtain a differential equation which characterizes a general (${\alpha},\;{\beta}$)-metric with isotropic E-curvature, under a certain condition. We also solve the equation in a particular case.

• 대한수학회보
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• 제61권1호
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• pp.281-290
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• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• 대한수학회논문집
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• 제17권2호
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• pp.279-293
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• 2002

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

• 대한기계학회논문집
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• 제11권3호
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• pp.444-453
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• 1987

본 연구에서는 난류구조에 대한 유선곡률의 영향을 명확히 반영하는 적절한 곡률수정 2-방정식모델을 개발하고자 한다. 이 연구에서 제안된 모델의 타당성은 다 음의 2차원 재순환유동에 대한 실험결과와 계산결과의 비교를 통해서 입증될 것이다. (1) Moss와 Bake에 의하여 맥동열선 풍속계로 측정된 두꺼운 수직벽주위의 유동` (2) 레이저 도플러 속도계로 Fraser와 Siddig에 의해 측정된 얇은 수직벽유동` (3)맥동열 선 풍속계로 Eaton이 실험한 후면벽유동` (4)맥동열선 풍속계로 Moss와 Baker가 측정 한 전면벽유동. 새로운 곡률수정 2-방정식모델은 2장에서 설명되고 있으며, 3장에서 는 경계조건과 수치계산 과정이 간단이 기술되어 있다. 그 뒤에 4장에는 계산결과와 실험치에대한 비교검토가 설명되어 있고 마지막으로 5장에서는 본 연구에 대한 결론을 맺고 있다.

• 대한수학회논문집
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• 제20권4호
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• pp.775-779
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• 2005

On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.79-86
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• 2011

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by $-K{\leq}0$ and (N, $\bar{g}$) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : $M{\times}[0,{\infty}){\rightarrow}N$ be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

• 대한수학회지
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• 제55권6호
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• pp.1459-1468
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• 2018

We show that an umbilic-free minimal surface in ${\mathbb{R}}^3$ belongs to the associate family of the catenoid if and only if the geodesic curvatures of its lines of curvature have a constant ratio. As a corollary, the helicoid is shown to be the unique umbilic-free minimal surface whose lines of curvature have the same geodesic curvature. A similar characterization of the deformation family of minimal surfaces with planar lines of curvature is also given.

• 대한수학회논문집
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• 제34권3호
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• pp.911-920
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• 2019

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension n = 4, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type I, D or O and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

• 호남수학학술지
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• 제29권4호
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• pp.641-647
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• 2007

In this paper, we consider the problem of achieving constant scalar curvature on warped product manifolds according to fiber manifolds with constant scalar curvature.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.91-100
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• 2013

This paper is a direct continuation of [1] and [2]. In this paper we investigate some properties of ES-curvature tensor and contracted ES-curvature tensor of g - $ESX_n$. Also, we study the field equations in the n-dimensional ES manifold g - $ESX_n$.