• 대한수학회보
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• 제35권2호
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• pp.195-201
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• 1998

We let (M,g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvatue S, which is close to -1. We show the existence of a conformal metric $\bar{g}$, near to g, whose scalar curvature $\bar{S}$ = -1 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_i$ with ${\bigcup}K_i$ = M.

• 대한수학회보
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• 제50권2호
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• pp.537-542
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• 2013

• 대한수학회보
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• 제50권5호
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• pp.1567-1586
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• 2013

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.

• 대한수학회보
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• 제49권3호
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• pp.655-667
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• 2012

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

• 대한수학회지
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• 제61권1호
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.109-124
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• 2011

The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

• 호남수학학술지
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• 제28권1호
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• pp.141-164
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• 2006

Let $G=O(2){\times}O(2){\times}O(2)$ and let $M^4$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$. In this paper, we prove a property on $M^4$.

• 대한수학회보
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• 제55권2호
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• pp.331-340
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• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• 한국가스학회지
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• 제14권3호
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• pp.46-52
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• 2010

삼지화염의 화염안정화 메커니즘 중 중요한 한 가지는 화염전파속도이다. 화염전파속도의 정량적인 규명을 위해 Bilger는 층류 유동이론에 근거하여 혼합분율 기울기에 비선형적으로 연관된 삼지화염전파속도를 제시하였다. 그러나 지금까지의 연구에서는 화염의 곡률 반경과 스칼라소산율에 따른 삼지화염 전파속도에 관하여 논의된 바가 없으며, 본 논문에서는 수치해석을 통해 화염전파속도에 따른 화염의 곡률반경과 스칼라소산율의 관계를 살펴보았다. 본 논문의 결과로 연료의 노즐 출구속도에 따라 화염전파속도가 거의 선형적으로 변화됨을 알 수 있었다. 또 화염전파속도에 따라 스칼라소산율은 비선형적인 감소를 보였으며, 곡률반경은 거의 선형적인 변화를 보임을 알 수 있었다. 또 스칼라소산율에 따른 곡률 반경의 경우 비선형적인 감소를 보였다. 따라서 화염전파속도와 스칼라소산율 및 화염의 곡률반경 사이에 직접적인 연관성이 있는 것을 확인하였다.

• 대한수학회보
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• 제35권3호
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• pp.563-570
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• 1998

We makes an explicit description of compact 4-dimensional nilmanifolds as principal torus bundles and show that they are sysmplectic. We discuss some consequences of this and give in particular a Seibebrg-Witten-invariant proof of a Grovmov-Lawson theorem that if a compact 4-dimensional nilmanifold admits a metric of zero scalar curvature, then it is diffeomorphic to 4-tours, $T^4$.