• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.55-65
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• 2005

We find the expression of the curvature tensor field for a manifold with is endowed with an almost contact structure satisfying the condition (1.7). By using this condition we obtain some properties of the Ricci tensor and scalar curvature (d. Theorem 3.2 and Proposition 3.2).

• Honam Mathematical Journal
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• v.36 no.4
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• pp.795-803
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• 2014

In this paper, we decompose the curvature tensor (field) on the Abbena-Thurston manifold into three curvature-like tensor fields, and investigate geometric properties.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.155-169
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• 2009

In this paper, we mainly discuss factorable surfaces in 3-dimensional Minkowski space and give classification of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.113-125
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• 2019

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.841-852
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• 2019

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for p > n/2) have bounded diameter and finite fundamental group.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.623-636
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• 2023

In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or m-Bakry-Émery-Ricci curvature bounded from below.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1261-1269
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• 2023

For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.281-290
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• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• Journal of radiological science and technology
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• v.30 no.4
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• pp.335-341
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• 2007

General anatomy classifies diaphragm as muscle of boundary between chest and abdomen, while radiology divides it into right and left hemidiaphragm, because it is more advantageous in radiological diagnosis on chest and abdomen. Based on these anatomic characteristics of diaphragm, this study aimed to measure the height and curvature of right and left diaphragm in simple chest radiography. As a result, this study came to the following conclusions : 1. For all subjects who joined this study, it was found that their mean transverse diameter in internal diameter of thorax(ID) amounted to 293.3 mm(min. 221.0 mm, max 335.3 mm). 2. For the right and left height of diaphragm, it was found that 81.4% showed higher right diaphragm ; 16.2% showed equivalent height between right and left diaphragm ; and only 2.4% showed higher left diaphragm. 3. For higher right diaphragm, it was found that the mean height of right diaphragm amounted to 15.2 mm(min. height = 2.0 mm, max. height = 41.7 mm). 4. For higher left diaphragm, it was found that the mean height of left diaphragm amounted to 11.5 mm(min. height = 4.7 mm, max. height = 30.4 mm). 5. The mean curvature of right diaphragm amounted to 22.9 mm(min. curvature = 10.4 mm, max. curvature = 37.3 mm). 6. The mean curvature of left diaphragm amounted to 22.4 mm(min. curvature = 11.3 mm, max. curvature = 42.2 mm). 7. For possible associations between ID and right/left diaphragm curvature, it was noted that ID was in significantly positive correlations with right diaphragm curvature(r= .427, p<.001) and left diaphragm curvature(r= .425, p<.001) on statistical level. 8. For possible associations between right and left diaphragm curvature, it was found that right diaphragm curvature was in significantly positive correlations with left diaphragm curvature(r= .403, p<.001).

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.3
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• pp.59-65
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• 2004

In this paper a numerical study was performed for the effect of the wall curvature on the behaviors of fuel sprays impinging on the concave Surface. Actually, in the real diesel engines, a piston head has a curved shape for the purpose of the controlling the movement of fuel droplets and the mixture formation. For past decades, although many experimental and numerical works had been performed on the spray/wall impingement phenomena, the curvature effect of impinged wall was rarely investigated. The wall curvature affects on the behaviors of the secondary droplets generated by impingement and the concave wall obstructs the droplets to advance from the impinging site to outward. In present study, the simulation code was validated for the flat surface case and three cases of the different curvature were calculated and compared with the flat surface case for several parameters, such as the spray radius, the spray height and the position of vortex center of gas phase. The simulation results showed that the radial advance of the wall spray and the vortex is decreased with increasing the curvature. It was concluded that the curvature of the impinged wall significantly affects the behaviors of both the gas-phase and the droplet-phase.