• Honam Mathematical Journal
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• v.45 no.2
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• pp.248-268
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• 2023

As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.607-629
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• 2022

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝⁿ, g₀) → (Nⁿ, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.121-130
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• 2022

In this paper, we prove that every semi-conformal harmonic map between Riemannian manifolds is L-harmonic map. We also prove a Liouville type theorem for L-harmonic maps.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.655-663
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• 2005

One of the basic questions concerning harmonic map is on the existence of harmonic maps satisfying a certain condition. Rigidity of a certain harmonic map can be considered as an answer for this kinds of questions. In this article, we study a rigidity property of harmonic diffeomorphisms under the condition that the inverse map is also harmonic. We show that every such a harmonic diffeomorphism is totally geodesic or conformal in two dimensional case.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.201-207
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• 1996

If a torus has $L^p$-bounded second fundamental form then it is included in the lower part of the moduli space. That is, its conformal class is bounded.

• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.312-316
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• 2010

Conformal mapping has been a familiar tool of science and engineering for generations. The methods of numerical mapping are usually classified into those which construct the map from standard domain such as the unit disk onto the 'problem domain', and those which construct the map in the reverse direction. We treat numerical conformal mapping from the unit disk onto the Jordan regions as the problem domain in this paper. The traditional standard methods of this type are based on Theodorsen integral equation. Wegmann's method is well known as a Newton-like efficient one for solving Theodorsen equation. An improved method for convergence by applying low frequency pass filter to the Wegmann's method was proposed. In this paper we propose an effective algorithm for numerical conformal mapping based on the improved method. This algorithm is able to determine the discrete numbers and initial values automatically in accordance with the given region and the required accuracy. This results come from analyzing the shape of given domain as seen in the Fourier Transform.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.595-602
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• 2006

Determinations of conformal map from the unit disk onto a Jordan region are reduced to solve the Theodorsen equation which is an integral equation for the boundary correspondence function. Among numerical conformal maps the Wegmann's method is well known as a Newton efficient one for solving Theodorsen equation. However this method has not so wide class of convergence. We proposed as an improved method for convergence by applying a low frequency filter to the Wegmann's method. In this paper, we investigate error analysis and propose an automatic algorithm based on this analysis.

• 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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.16 no.2
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• pp.337-343
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• 1998

In Korea, map coordinates has been confused in use since the map projection system has been complicated by using two different methods i.e., Gauss conformal double projection and Gauss-Kruger projection which are com-plicated in using through history. So, we have to understand the two projections' characteristics and differences. In this study, we would find out a fact that the maximum difference occurred in longitude and latitude is about 15cm at the Korean peninsular. This shift is accepted as proper in GIS and cartographic application but should be considered carefully in converting of the geodetic control point coordinates.