• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.67-72
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• 2011

This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.359-366
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• 2009

In this paper, we study a tube in a Euclidean 3-space satisfying some equation in terms of the Gaussian curvature, the mean curvature and the second Gaussian curvature.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.603-624
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• 2015

We first extend the notions of weighted curvatures, including the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curvature bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curvature and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.701-706
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• 1999

A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature $H_1$ does not vanish and the ratio $H_n$/$H_1$ of the Gauss-Kronecker curvature $H_n$ and $H_1$ is constant.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.625-633
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• 2002

Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.639-648
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• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1367-1382
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• 2020

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.