• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.977-991
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• 2012

Let (M,F) and (M',F') be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F' is nonpositive, then any transversally harmonic map ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.79-86
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• 2011

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by $-K{\leq}0$ and (N, $\bar{g}$) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : $M{\times}[0,{\infty}){\rightarrow}N$ be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.547-552
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• 2003

In mold machining, there are many concave machining regions where chatter and tool deflection occur since MRR (material removal rate) increases as curvature increases even though cutting speed and depth of cut are constant. Boolean operation between stock and tool model is widely used to compute MRR in NC milling simulation. In finish cutting, the side step is reduced to about 0.3mm and tool path length is sometimes over 300m. so Boolean operation takes long computation time and includes much error if the resolution of stock and tool model is larger than the side step. In this paper, curvature of CL(cutter location) surface and side step of tool path is used to compute the feedrate for constant MRR machining. The data structure of CL surface is Z-map generated from NC tool path. The algorithm to get local curvature from discrete data was developed and applied to compute local curvature of CL surface. The side step of tool path was computed by point density map which includes cutter location point density at each grid element. The feedrate computed from curvature and side step is inserted to new tool path to regulate MRR. The resultants wire applied to feedrate optimization system which generates new tool path with feedrate from NC codes for finish cutting. The system was applied to speaker mold machining. The finishing time was reduced to 12.6%. tool wear was reduced from 2mm to 1.1mm and chatter marks and over cut on corner were removed.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.803-814
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• 1995

Let $\Sigma$ be the class of all complex-valued, harmonic, orientation-preserving, univalent mappings defined on $\Delta = {z : $\mid$z$\mid$ > 1}$ that map $\infty$ to $\infty$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.23-27
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• 2005

In this paper, we study rotation surfaces in a Euclidean space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem for rotation surfaces of constant mean curvature.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1007-1021
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• 2004

In this paper, we study rotation surfaces in the Minkowski 3-dimensional space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem concerning rotation surfaces and constancy of the mean curvature of certain open subsets on these surfaces.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.865-879
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• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.301-312
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• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.369-377
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• 2011

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that GSCS's with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only polynomial kind GSCS's with pointwise 1-type Gauss map of the second kind.