• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.619-632
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• 2017

We define a new connection on semi-Riemannian manifold, which is called a non-metric ${\phi}$-symmetric connection. Semi-symmetric non-metric connection and quarter-symmetric non-metric connection are two impotent examples of this connection. The purpose of this paper is to study the geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric ${\phi}$-symmetric connection.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1075-1089
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• 2018

We define a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. We say that this connection is an (${\ell}$, m)-type connection. Semi-symmetric non-metric connection and non-metric ${\phi}$-symmetric connection are two important examples of this connection such that (${\ell}$, m) = (1, 0) and (${\ell}$, m) = (0, 1), respectively. In this paper, we study lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (${\ell}$, m)-type connection.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.119-133
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• 2017

In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.101-115
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• 2017

In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.73-90
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• 2012

We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.821-828
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• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1297-1302
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• 2013

We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.327-339
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• 2012

In this paper we study $h$-projectively semisymmetric, ${\phi}$-pro-jectively semisymmetric, $h$-Weyl semisymmetric and ${\phi}$-Weyl semisym- metric non-Sasakian ($k$, ${\mu}$)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, ${\mu}$)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.7
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• pp.100-114
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• 1996

In order to create a solid model more efficiently for a plastic or sheet metal product with a thin and constant thickness, various methods have been proposed up to now. One of the most typical approaches is to create a sheet model initially and then transform it into a solid model automatically for a given thickness. The sheet model as well as the transitive model in sheet modeling procedure is a non-manifold model. However, the previous methods adopted the boundary representations for a solid model as their topological framework. Thus, it is difficult to represent the exact adjacency relationship between topological entities and to implement the topological operations for sheet modeling and the transformation procedure of a sheet into a solid. In this paper, we proposed a sheet modeling system based on a non-manifold topological representation which can represent solids, sheets, wireframes, and their mixture. A set of generalized Euler operators for non-manifold topology as well as the sheet modeling capabilities including adding, bending, and punching functions are provided for easy modeling of sheet objects, and they are perfomed interactively with a two dimensional curve editor. Once a sheet model is completed, it can be transformed into a solid automatically. The transformation procedure is composed of the offset functions and the Boolean operations of sheet models, and it is even more comprehensive and easier to be implemented than the precious methods.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.242-254
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• 2000

This paper describes an efficient solid modeling method for thin-walled plastic or sheet metal parts, based on the non-manifold offsetting operations. Since the previous methods for modeling and converting a sheet into a solid have adopted the boundary representations for solid object as their topological framework, it is difficult to represent the exact adjacency relationship between topological entities of a sheet model and a mixture of wireframe and sheet models that can appear in the meantime of modeling procedure, and it is hard to implement topological operations for sheet modeling and transformation of a sheet into a solid. To solve these problems, we introduce a non-manifold B-rep and propose a sheet conversion method based on a non-manifold offset algorithm. Because the non-manifold offset aigorithm based on mathematical definitions results in an offset solid with tubular and spherical thickness-faces we modify it to generate the ruled or planar thickness-faces that are mostly shown in actual plastic or sheet metal parts. In addition, in order to accelerate the Boolean operations used the offset algorithm, we also develope an efficient face-face intersection algorithm using topological adjacency information.