• 한국수학사학회지
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• 제28권2호
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• pp.103-115
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• 2015

Contemporary differential geometry owes much to the theory of connections on the bundles over manifolds. In this paper, following the work of Gauss on surfaces in 3 dimensional space and the work of Riemann on the curvature tensors on general n dimensional Riemannian manifolds, we will investigate how differential geometry had been developed from mid 19th century to early 20th century through lives and mathematical works of Christoffel, Ricci-Curbastro and Levi-Civita. Christoffel coined the Christoffel symbol and Ricci used the Christoffel symbol to define the notion of covariant derivative. Levi-Civita completed the theory of absolute differential calculus with Ricci and discovered geometric meaning of covariant derivative as parallel transport.

• 대한수학회논문집
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• 제35권4호
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• pp.1075-1085
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• 2020

We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor P : Mod-R → Spec(Mod-R), where Spec(Mod-R) denotes the spectral category of Mod-R, and the localization functor with respect to the singular torsion theory.

• East Asian mathematical journal
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• 제26권1호
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• pp.75-79
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• 2010

Let G be a compact connected semisimple Lie group, g the Lie algebra of G, g the canonical metric (the biinvariant Riemannian metric which is induced from the Killing form of g), and $\nabla$ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection $\nabla$ in the tangent bundle TG over (G, g) is a Yang-Mills connection.

• 충청수학회지
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• 제23권4호
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• 한국수학교육학회지시리즈A:수학교육
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• 제23권2호
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• pp.67-69
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• 1985

• 충청수학회지
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• 제25권4호
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• pp.599-608
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• 2012

In [2], [8], the author studied the characteristic connection as a good substitute for the Levi-Civita connection. In this paper, we consider the space $U(3)=(U(1){\times}U(1){\times}U(1))$ with an almost Hermitian structure which admits a characteristic connection and compute the characteristic connection concretely.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.105-116
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• 2018

In this paper, the object is to study a semi-symmetric non-metric connection on an LP-Sasakian manifold whose concircular curvature tensor satisfies certain curvature conditions.

• East Asian mathematical journal
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• 제14권2호
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• pp.317-320
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• 1998

The main result is that the connection form in the orthonormal frame bundle by the Levi-Civita connection over a Riemannian symmetric space is a Yang-Mills connection

• 한국멀티미디어학회논문지
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• 제16권2호
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• pp.160-168
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• 2013

본 논문에서는 단순 폐곡선으로 구성된 형태열을 형태 다양체의 기하학적 특성에 따라 평행한 무빙 프레임으로 표현하는 기법을 개발한다. 형태 다양체는 기본적으로 유클리드 공간이 아니어서 형태열(곡선)에서 구한 접벡터의 변화율 등을 측정하기가 매우 어렵다. 레비 치비타 접속(Levi-Civita connection) 이론에 의하면 무빙 프레임을 주어진 형태열에 따라 평행 이동할 수 있으면 공변미분을 통하여 접벡터장의 변화율을 측정하는 것이 가능하다. 따라서 본 논문에서는 주 프레임 다발(principal frame bundle)의 개념을 도입하여 비유클리드 공간의 형태열의 접벡터를 유클리드 공간으로 평행 이동시키는 툴을 구현하고 실험을 통하여 이의 특성을 확인하고 분석한다.

• 충청수학회지
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• 제26권4호
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• pp.843-852
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• 2013

The characteristic connection is a good substitute for Levi-Civita connection in studying non-integrable geometries. In this paper we consider the homogeneous space $U(3)/(U(1){\times}U(1){\times}U(1))$ with a one-parameter family of Hermitian structures. We prove that the one-parameter family of Hermtian structures admit a characteristic connection. We also compute the torsion of the characteristic connecitons.