• 충청수학회지
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• 제21권3호
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• pp.371-376
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• 2008

Let $P(M,G,{\pi})=:P$ be a principal fibre bundle with structure Lie group G over a base manifold M. In this paper we get the following facts: 1. The tangent bundle TG of the structure Lie group G in $P(M,G,{\pi})=:P$ is a Lie group. 2. The Lie algebra ${\mathcal{g}}=T_eG$ is a normal subgroup of the Lie group TG. 3. $TP(TM,TG,{\pi}_*)=:TP$ is a principal fibre bundle with structure Lie group TG and projection ${\pi}_*$ over base manifold TM, where ${\pi}_*$ is the differential map of the projection ${\pi}$ of P onto M. 4. for a Lie group $H,\;TH=H{\circ}T_eH=T_eH{\circ}H=TH$ and $H{\cap}T_eH=\{e\}$, but H is not a normal subgroup of the group TH in general.

• 대한수학회지
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• 제55권3호
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• 대한수학회논문집
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• 제14권1호
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• pp.211-216
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• 1999

We study the anti-linear involutions on a real algebraic vector bundle with bundle with a compact real algebraic group action.

• 충청수학회지
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• 제33권3호
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• pp.365-374
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• 2020

Given a noncompact semisimple Lie group G and its maximal compact Lie subgroup K such that the right multiplication of each element in K gives an isometry on G, consider a principal bundle G → G/K, which is a Riemannian submersion. We study the infinitesimal holonomy isometries. Given a closed curve at eK in the base space G/K, consider the holonomy displacement of e by the horizontal lifting of the curve. We prove that the correspondence is continuous.

• 대한수학회보
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• 제33권3호
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• pp.477-480
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• 1996

Let $\pi : Z \longrightarrow Y$ be a fiber bundle where Y and Z are compact Riemannian manifolds without boundary. We are primarily interested in the case where $\pi$ is a Riemannian submersion with minimal fibers; this is the case, for example, where Z is the sphere bundle of some vector bundle over Y or where Z is a principal bundle over Y.

• 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.

• 대한수학회보
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• 제36권4호
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• pp.649-654
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• 1999

We consider the forgetful map from the group of equivariant self equivalences to the group of non-equivariant self equivalences. A sufficient condition for this forgetful map being a monomorphism is obtained. Several examples are given.

• 소성∙가공
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• 제18권4호
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• pp.342-346
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• 2009

Forming characteristics for the bundle extrusion of Cu-Ti bimetal wires are investigated, which can identify the process conditions for weak mechanical bonding at the contact surface during the direct extrusion of a Cu-Ti bimetal wire bundle. Bonding mechanism between Cu and Ti is assumed as a cold pressure welding. Then, the plastic deformation at the contact zone causes mechanical bonding and a new bonding criterion for pressure welding is developed as a function of the principal stretch ratio and normal pressure at the contact surface by analyzing micro local extrusion at the contact zone. The averaged deformation behavior of Cu-Ti bimetal wire is adopted as a constitutive behavior at a material point in the finite element analysis of Cu-Ti wire bundle extrusion. Various process conditions for bundle extrusions are examined. The deformation histories at the three points, near the surface, in the middle and near the center, in the cross section of a bundle are traced and the proposed new bonding criterion is applied to predict whether the mechanical bonding at the Cu-Ti contact surface happens. Finally, a process map for the direct extrusion of Cu-Ti bimetal wire bundle is proposed.

• Kyungpook Mathematical Journal
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• 제31권1호
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• pp.25-34
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• 1991

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2005년도 추계학술대회 논문집
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• pp.393-397
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• 2005

A process map has been developed, which can identify the process conditions for weak mechanical bonding at the contact surface during the direct extrusion of a Cu-Ti bimetal wire bundle. Bonding mechanism between Cu and Ti is assumed as a cold pressure welding. Then, the plastic deformation at the contact zone causes mechanical bonding and a new bonding criterion fur pressure welding is developed as a function of the principal stretch ratio and normal pressure at the contact surface by analyzing micro local extrusion at the contact zone. The averaged deformation behavior of Cu-Ti bimetal wire is adopted as a constitutive behavior at a material point in the finite element analysis of Cu-Ti wire bundle extrusion. Various process conditions for bundle extrusions are examined. The deformation histories at the three points, near the surface, in the middle and near the center, in the cross section of a bundle are traced and the proposed new bonding criterion is applied to predict whether the mechanical bonding at the Cu-Ti contact surface happens. Finally, a process map for the direct extrusion of Cu-Ti bimetal wire bundle is proposed.