• Korean Journal of Mathematics
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• v.13 no.1
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• pp.51-59
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• 2005

Let (M, $g$) be a compact oriented self-dual 4-dimensional Einstein manifold with positive sectional curvature. Then we show that, up to rescaling and isometry, (M, $g$) is $S^4$ or $\mathbb{C}\mathbb{P}_2$, with their cannonical metrics.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.482-487
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• 2002

This paper presents a robot trajectory generation method based on the dual curvature theory of ruled surfaces. Robot trajectory can be represented as a ruled surface generated by the TCP(Tool Center Point) and my unit vector among the tool frame. Dual curvature theory of ruled surfaces provides the robot control algorithm with the motion property parameters. With the differential properties of the ruled surface, the linear and angular motion properties of the robot end effector can be utilized in the robot trajectory planning.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.851-864
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• 2022

We define a kind of sectional curvature and 𝛿-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.471-490
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• 2023

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇^* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R^* of the connections ∇ and ∇^* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇^*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1339-1355
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• 2006

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.1
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• pp.70-76
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• 2015

The ship hull is accomplished by assembling various curved surfaces. There are numerous existing methods for ship hull processing, which need certain appropriate processing methods to enable it to be more efficient. The curved hull plates can be divided into convex region and saddle region. It is common to use line heating method to form a saddle region, when it comes to a convex region, it will be triangle heating method to be utilized. A precise analysis for curvature domain is required for the application of proper processing method. There exist various problems on existing calculation methods of curvature domain. Therefore, a more powerful method is demanded to it more accurately. In this study, a method called Dual Contouring is applied to extract curved surfaces, which is able to improve accuracy of extracted area. Based on all above, a best-suited heat processing method should be selected.

• Journal of the Korean Mathematical Society
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• v.28 no.1
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• pp.87-97
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• 1991

• Journal of the Korean institute of surface engineering
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• v.47 no.6
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• pp.362-367
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• 2014

We report the design, fabrication of a $Si_3N_4$ probe and calculation of its mechanical properties for DPN(dip pen nanolithography), which consists of dual tips. Concept of dual tip probe is to employ individual tips on probe as either an AFM tip for imaging or a writing tip for nano patterning. For this, the dual tip probe is fabricated using low residual stress $Si_3N_4$ material with LPCVD deposition and MEMS fabrication process. On the basis of FEM analysis we show that the functionality of dual tip probe for imaging is dependent on the dimensions of dual tip probe, and high ratio of widths of beam areas is preferred to minimize curvature variation on probe.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.109-122
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• 2003

In this paper we give a characterization of an irreducible connection with harmonic curvature over a connected Kaehler manifold to be self-dual. Also we introduce new notions of $c_{i}-self-dual$ or Kaehler Yang-Mills connections on compact Kaehler manifolds and investigate some fundamental properties of this kind of new connections. Moreover, on a compact odd dimensional Riemannian manifold we give a property of generalized monopole.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.739-753
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• 2014

In this study, it is aimed to analyze how relationship among Blaschke vectors that the obtained formulae in [2, 3] change if parameter ruled surfaces of the spacelike line congruence are not choosed as principle ruled surfaces. Moreover, using the relation among Blaschke vectors, we obtain Manheim's and Liouville's formulae. This new method can be applied to congruences. Thus, we can obtain new formulae in lines space.