• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.493-511
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• 2008

In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let $\varphi:(M^n,g)\rightarrow(N^m,h)$ be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of $\varphi$. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, $\varphi^{-1}$(P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.100-114
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• 1996

In this paper, a new thin-walled beam finite elcment is developed to overmome the difficulties in the analysis of real structures by existing beam elements. The element is formulated by extending Benscoter's assumption and also by adopting the concept of the curvature-based element. It is applicable to the analysis of the beams with arbitrary cross-sectional shapes. The results obtained show that the element is locking-free and the accuracy of the finite element solutions is remarkably improved.

• Transactions of Materials Processing
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• v.15 no.2 s.83
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• pp.126-131
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• 2006

Metallic sandwich plates are ultra-light materials not only with high strength and stiffness but also with other multifunctional physical properties. Inner dimpled shell structure can be fabricated by a piecewise sectional forming process, and then bonded with face sheets of the same material by resistance welding. Possible region for bending and limit radius of curvature are defined to compare the formability of sandwich plates. Tests have shown that sandwich plates with inner dimpled shell structure subject to bending have longer possible region for bending and smaller limit radius of curvature than other types of sandwich plates. The proposed inner dimpled shell structure is shown to have better formability of sandwich plates for bending than other types inner structures.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.57-69
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• 2002

We study a unifying method to obtain nondegenerate isometric immersions of manifolds of constant sectional curvatures c with flat normal bundles into the space forms of curvature c for c= -1,0,1.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.419-428
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• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.713-720
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• 2009

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.101-119
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• 1996

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.253-263
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• 2001

Niebergall and Ryan posed some open questions on 3-dimensional real hypersurfaces in complex space forms. In this paper we give affirmative answers to such kind of questions.

• Magazine of the Korea Concrete Institute
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• v.11 no.1
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• pp.99-107
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• 1999

In this paper, the prediction method of the differential column shortening for cracked reinforced concrete tall buildings due to the construction sequence is presented. The cracked sectional properties from the strain and curvature of the sectional centroid is directly used. And the stiffness matrix of concrete elements considering the axial strain-curvature interaction effect is adopted. The creep and shrinkage properties used in the predictions were calculated in accordance with ACI 209, CEB-FIP 1990, and B3 model code. In order to demonstrate the validity of this algorithm, the prediction by the proposed method are compared with both the results of the in-situ test and the results by other simplified method. The proposed method is in good agreement with experimental results, and better than the simplified method.