• Honam Mathematical Journal
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• v.42 no.3
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• pp.461-476
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• 2020

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1101-1110
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• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.223-228
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• 2015

In this paper, we study the eigenvalue problem of Schr$\ddot{o}$dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.169-178
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• 2019

Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.135-141
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• 2004

We studied the relation between the tangential Cauchy-Riemann operator ${\={\partial}}_b$ CR-manifolds and the derivation $d^{{\pi}^{0,\;1}}$ associated to the natural projection map ${\pi}^{0.1}\;:\;TM\;{\bigotimes}\;{\mathbb{C}}\;=\;T^{1,0}\;{\bigoplus}\;T^{0,\;1}\;{\rightarrow}\;T^{0,\;1}$. We found that these two differential operators agree only on the space of functions ${\Omega}^0(M),\;unless\;T^{1,\;0}$ is involutive as well. We showed that the difference is a derivation, which vanishes on ${\Omega}^0(M)$, and it is induced by the Nijenhuis tensor associated to ${\pi}^{0.1}$.

• Journal of the Korean Society for Heat Treatment
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• v.34 no.1
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• pp.10-16
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• 2021

Exhaust manifold is a very important component that is directly connected to air environment pollution and that requires strict mechanical properties such as high temperature fatigue and oxidation. Among stainless steels, the ferritic stainless steel with body-centered cubic structure shows excellent resistance of stress-corrosion cracking, ferromagnetic at room temperature, very excellent cold workability and may not be enhanced by heat treatment. The microstructural characteristics of four cast ferritic stainless steels which are high heat-resistant materials, were analyzed. By comparing and evaluating the mechanical properties at room temperature and high temperature in a range of 400℃~800℃, a database was established to control and predict the required properties and the mechanical properties of the final product. The precipitates of cast ferritic stainless steels were analyzed and the high-temperature deformation characteristics were evaluated by comparative analysis of hardness and tensile characteristics of four steels at room temperature and from 400℃ to 800℃.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.101-125
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• 2001

This is a survey article on almost Lorentzian paracontact manifolds. The study of Lorentsian almost paracontact manifolds was initiated by Matsumoto [On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-l56]. Later on several authors studied Lorentzian almost paracontact manifolds and their different classes, viz. LP-Sasakian and LSP-Sasakian manifolds. Different types of submanifolds, for example invariant, semi-invariant and almost semi-invariant, of Lorentzian almost paracontact manifold have been studied. Here, we present a brief survey of results on Lorentzian almost paracontact manifolds with their different classes and their different kind of submanifolds.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1211-1223
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• 2016

Let M be an n-dimensional $K{\ddot{a}}hler$ manifold with positive holomorphic bisectional curvature and let ${\Omega}{\Subset}M$ be a pseudoconvex domain of order $n-q$, $1{\leq}q{\leq}n$, with $C^2$ smooth boundary. Then, we study the (weighted) $\bar{\partial}$-equation with support conditions in ${\Omega}$ and the closed range property of ${\bar{\partial}}$ on ${\Omega}$. Applications to the ${\bar{\partial}}$-closed extensions from the boundary are given. In particular, for q = 1, we prove that there exists a number ${\ell}_0$ > 0 such that the ${\bar{\partial}}$-Neumann problem and the Bergman projection are regular in the Sobolev space $W^{\ell}({\Omega})$ for ${\ell}$ < ${\ell}_0$.

• Journal of Welding and Joining
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• v.27 no.5
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• pp.49-54
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• 2009

Recently, a demand of ferritic STS is increasing rapidly in automobile exhaust system. Exhaust manifolds are the part nearest to the engine so that the material is exposed to high temperature exhaust gas. Excellent heat resistant properties, especially high temperature strength, thermal fatigue resistance and high corrosion resistance are necessary for these parts. STS429L contains 15 weight percent of Cr and low Mo, so has good price competitive. And it has excellent high temperature strength and corrosion resistance, so receives attentions as material that applying to exhaust manifold. In tensile test of lap joint welded STS 429L, most of specimens are failed in base metal, but occurs brittle fracture in weld metals at some specimens in the face of good welding conditions. In the process of tensile test, lap joint welded STS429L specimens are transformed locally. The brittle fracture occurs that local transforming area exists in weld metals. But, butt welding specimens made by same materials showed ductile fracture in tensile test and bending test. In this study, suppose the reason of brittle fracture is in the combined local transform and tensile stress, through analysis of bead geometry, evaluate geometrical factor of brittle fracture in lap joint welded STS429L.