• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.133-149
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• 1996

In order to reduce the trial-and-errors in design and production of injection molded plastic parts, there has been much research effort not only on CAE systems which simulate the injection molding process, but also on CAD systems which support initial design and re-design of plastic parts and their molds. The CAD systems and CAE systems have been developed independently with being built on different basis. That is, CAD systems manipulate the part shapes and the design features in a complete solid model, while CAE systems work on shell meshes generated on the abstract sheet model or medial surface of the part. Therefore, it is required to support the two types of geometric models and feature information in one environment to integrate CAD and CAE systems for accelerating the design speed. A feature-based non-manifold geometric modeling system has been developed to provide an integrated environment for design and analysis of injection molding products. In this system, the geometric models for CAD and CAE systems are represented by a non-manifold boundary representation and they are merged into a single geometric model. The suitable form of geometric model for any application can be extracted from this model. In addition, the feature deletion and interaction problem of the feature-based design system has been solved clearly by introducing the non-manifold Boolean operation based on 'merge and selection' algorithm. The sheet modeling capabilities were also developed for easy modeling of thin plastic parts.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.895-903
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• 2009

We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.505-517
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• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1171-1180
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• 2022

The object of the present paper is to study the properties of conharmonically flat (LCS)_n-manifold, special weakly Ricci symmetric and generalized Ricci recurrent (LCS)_n-manifold. The existence of such a manifold is ensured by non-trivial example.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.713-724
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• 2005

We prove that a (k, $\mu$)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, $\mu$)­manifolds with C-Bochner curvature tensor B satisfying B $(\xi,\;X)\;\cdot$ S = 0, where S is the Ricci tensor, are classified. N(K)-contact metric manifolds $M^{2n+1}$, satisfying B $(\xi,\;X)\;\cdot$ R = 0 or B $(\xi,\;X)\;\cdot$ B = 0 are classified and studied.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.235-244
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• 1999

We will derive some identities related to p-scalars, p-vectors, and non-holonomic frames in a generalized 2-dimensional Riemannian manifold $X_2$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1213-1219
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• 2009

Let M$^n$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold N$^{n+p}$ of nonnegative curvature. We prove that if M is super-stable, then there are no non-trivial L$^2$ harmonic one forms on M. This is a generalization of the main result in [8].

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.357-363
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• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.