• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.507-520
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• 2009

The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.883-899
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• 2014

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.207-216
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• 2014

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 3-dimensional $^*g-ESX_3$. Particularly, in 3-dimensional $^*g-ESX_3$, we derive a new set of powerful recurrence relations in the first class.

• Transactions of Materials Processing
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• v.14 no.3 s.75
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• pp.269-276
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• 2005

The purpose of this research is the warpage reduction for intake-manifold which is made to the injection molding. Intake-manifold is assembling to ultra sonic welding after forming. Therefore deformation is influence on the performance and manufacture to intake-manifold product. Location and number of gates, filling time, mold temperature, packing time, packing pressure and cooling time are factors that affect the deformation of injection molding product. Therefore, the injection molding characteristics of intake-manifold and the estimated deformation are detected by CAE analysis and compare measuring data in this study.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.3 s.258
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• pp.338-343
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• 2007

Thermal deformation of cast iron exhaust manifold for turbo diesel engine is investigated by finite element analysis (FEA). The FE model included the temperature dependent material properties as well as the interactions between exhaust manifold, cylinder head and fasteners. It also considers the sliding behavior of the flanges of exhaust manifold on cylinder head when either expansion or contraction of the exhaust manifold exceeds the fastener pretension. The result of analysis revealed that remarkable thermal deformation along the longitudinal direction. Compressive plastic deformation at high temperature remained tensile stress in manifold and resulted in longitudinal contraction at ambient temperature. The amount of contraction at each fastener position was predicted and compared with experimental results. Analysis results revealed that the model predicted deformation qualitatively, but more elaborated cyclic hardening behavior would be necessary to predict the deformation quantitatively.

• 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.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.435-445
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• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.475-487
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• 2003

A generalized even-dimensional Riemannian manifold defined by the ME-connection which is both Einstein and of the form (3.3) is called an even-dimensional ME-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an ME-connection, to derive the useful properties of some tensors, and to investigate a representation of the ME-vector in $MEX_{2n}$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.815-823
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• 1996

M. Kontsevich posed a problem on mapping class groups of 3-manifold that is if M is a compact 3-manifold with nonempty boundary, then BDiff (M rel $\partial$ M) has the homotopy type of a finite complex. Here, Diff (M rel $\partial$ M) is the group of diffeomorphisms of M which restrict to the identity on $\partial$ M, and BDiff (M rel $\partial$ M) is its classifying space. In this paper we resolve the problem affirmatively in the case when M is a Haken 3-manifold.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1321-1336
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• 2018

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian 3-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian 3-manifold is homothetic to either a Sasakian or cosymplectic 3-manifold.