• Journal of Korea Multimedia Society
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• v.6 no.6
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• pp.985-990
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• 2003

This paper presents the representation and its shape analysis of face by features based on surface curvature estimation and proposed rotation vector of the human face. Curvature-based surface features are well suited to use for experimenting the 3D human face segmentation. Human surfaces are exactly extracted and computed with parameters and rotated by using active surface mesh model. The estimated features were tested and segmented by reconstructing surfaces from the face surface and analytically computing Gaussian (K) and mean (H) curvatures without threshold.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.337-343
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• 2010

We study affine translation surfaces in $\mathbb{R}^3$ and get a complete classification of such surfaces with constant Gauss-Kronecker curvature.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.41-61
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• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.509-531
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• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.594-617
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• 2022

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.403-404
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• 2014

• Honam Mathematical Journal
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• v.46 no.1
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• pp.12-37
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• 2024

The paper introduces a set of new ruled surfaces such that the base curve is taken to be the striction curve of N, C and W ruled surfaces from the alternative frame, and the generating line is taken to be one of the vectors of Sannia frame. The characterizations for each ruled surface such as fundamental forms, the Gaussian and mean curvature are also examined to provide the conditions for each surface to be developable or minimal.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.79-85
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• 2003

We define the second Gausssian curvature $K_{II}$ by using Brioschi's formula and shall disscuss the helicoidal surfaces satisfying $K_{II}$=Η.

• East Asian mathematical journal
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• v.21 no.1
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• pp.113-122
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• 2005

Let $\mathbb{H}^3$ be the 3-dimensional Heisenberg group equipped with a left-invariant metric. In this paper, We characterize the Gaussian curvatures of the geodesic spheres on $\mathbb{H}^3$.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.151-167
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• 2016

In Minkowskian 3-spacetime $L^3$ we find timelike or spacelike surface of revolution for the given Gauss curvature K = -1, 0, 1 and mean curvature H = 0. In fact, we set up the surface of revolution with the time axis for z-axis to be able to draw those surfaces on standard pictures in Minkowskian 3-spacetime $L^3$.