• 대한수학회보
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• 제54권4호
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• pp.1293-1307
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• 2017

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

• 대한수학회논문집
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• 제34권1호
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• pp.303-319
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• 2019

The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.

• Kyungpook Mathematical Journal
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• 제29권2호
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• pp.167-186
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• 1989

• 대한수학회논문집
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• 제35권1호
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• pp.251-260
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• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• 대한수학회보
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• 제56권5호
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• pp.1219-1233
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• 2019

Let $E{\rightarrow}M$ be an arbitrary vector bundle of rank k over a Riemannian manifold M equipped with a fiber metric and a compatible connection $D^E$. R. Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on E. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on E in the case when $D^E$ is flat. We study also the Einstein property on E proving, among other results, that if $k{\geq}2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on E, which are not Ricci-flat.

• Journal of Welding and Joining
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• 제28권2호
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• pp.60-65
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• 2010

Although two dimensional axi-symmetric modeling is useful for calculating the residual stresses of a cylindrical weldment such as a core barrel, this conventional axi-symmetric modeling can not express the behavior of shrinkage well in the locally heated weld zone. New technique of two dimensional axi-symmetric modeling using a virtual fixture is suggested to simulate the behavior of dimensional changes in the weld zone during the heating period of the welding. The virtual fixture in the model has a role to restrain the expansion of the high temperature heated region, which simulates equivalent intrinsic restraint effect of the weldment. In the restraint condition of the virtual fixture above the critical yield strength, the calculated shrinkages by using the suggested axi-symmetric model agreed well with those measured in a welded mock-up. The calculated residual stresses by using the suggested axi-symmetric model also agreed well with those calculated by using conventional axi-symmetric model which has beenused for calculating residual stresses in the weldment.

• 호남수학학술지
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• 제38권2호
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• pp.375-384
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• 2016

In this paper, we study the pseudo-symmetry of unit tangent sphere bundle. We prove that if the unit tangent sphere bundle $T_1M$ with standard contact metric structure over a locally symmetric $M^n$, $n{\geq}3$ is pseudo-symmetric, then M is of constant curvature.

• 대한수학회보
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• 제51권1호
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.

• 대한수학회보
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• 제54권3호
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• pp.911-916
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• 2017

A Damek-Ricci space is a typical locally harmonic manifold, which is a generalization of the rank one symmetric space of the non-compact type. In this paper, we determine explicitly the characteristic function of a Damek-Ricci space by calculating the determinant of a Jacobi tensor.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.61-66
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• 2022

A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.