• 대한수학회보
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• 제58권5호
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• pp.1053-1068
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• 2021

We investigate the spacelike hypersurface Mⁿ with constant mean curvature (CMC) in a Lorentz Einstein manifold Lⁿ⁺¹₁, which is supposed to obey some appropriate curvature constraints. Applying a suitable Simons type formula jointly with the well known generalized maximum principle of Omori-Yau, we obtain some rigidity classification theorems and pinching theorems of hypersurfaces.

• 대한수학회지
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• 제56권6호
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• pp.1475-1488
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• 2019

In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^n,g)(n{\geq}3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.

• 대한수학회보
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• 제61권4호
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• pp.933-948
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• 2024

For (n ≥ 5)-dimensional compact V-static spaces with zero radial Weyl curvature, we prove that ∇f is an eigenvector of Ricci tensor. Furthermore, we also achieve that (Mⁿ, g, f) is T-flat provided $K{\frac{{\mid}{\nabla}{\mid}f^2}{f}}>0$.

• 한방재활의학과학회지
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• 제20권1호
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• pp.133-139
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• 2010

Objectives : The purpose of this study was to compare about quantity of pain and fatigue according to cervical spine curvature of patient with neck pain. Methods : Cervical spine curvature was measured using the sagittal radiography of the cervical spine, neck pain was evaluated using the VAS and neck fatigue was evaluated using fatigue symptom checklist. Based on four line Cobb's method, 51 subjects were divided into hypolordosis group, normal group, hyperlordosis group. Window version SPSS 12K was used for statistical analysis about relation between pain and cervical spine curvature of each group, also about between fatigue and cervical spine curvature of each group. Results : 1. A significant difference was not found between pain and cervical curvature of each group. 2. A significant difference was not found between fatigue and cervical curvature of each group. Conclusions : There was no relation between pain and cervical curvature of each group, also fatigue and cervical curvature.

• 대한수학회지
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• 제31권3호
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• 소음진동
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• 제11권1호
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• 대한수학회보
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• 제55권6호
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• pp.1891-1908
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• 2018

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{\(\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}\)^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

• 대한수학회지
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• 제50권6호
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• pp.1311-1332
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• 2013

This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

• 대한수학회지
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• 제49권5호
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• pp.977-991
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• 2012

Let (M,F) and (M',F') be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F' is nonpositive, then any transversally harmonic map ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

• 대한수학회보
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• 제56권1호
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• pp.253-263
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• 2019

Let M be a curvature homogeneous or ball-homogeneous non-$coK{\ddot{a}}hler$ almost $coK{\ddot{a}}hler$ 3-manifold. In this paper, we prove that M is locally isometric to a unimodular Lie group if and only if the Reeb vector field ${\xi}$ is an eigenvector field of the Ricci operator. To extend this result, we prove that M is homogeneous if and only if it satisfies ${\nabla}_{\xi}h=2f{\phi}h$, $f{\in}{\mathbb{R}}$.