• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.415-424
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• 2009

The object of the present paper is to study the generalized quasi-Einstein manifolds satisfying some conditions. Finally the existence of such manifolds is ensured by several interesting examples.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.43-50
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• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Korean Journal of Mathematics
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• v.10 no.2
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• pp.157-166
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• 2002

We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.25-29
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• 1992

The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.125-134
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• 2001

Independent $\sigma$-algebras Α and Β on X, L$^2$(X, Α V Β), L$^2$(X x X, Α x Β), and the Hilbert space tensor product L$^2$(X,Α), (※Equations, See Full-text) L$^2$(X,Β), are isomorphic. In this note, we show that various Hilbert C(sup)*-algebra tensor products provide the analogous roles when independence is weakened to conditional independence.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.165-165
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• 2001

Purpose： To obtain quantitative diffusion-tensor anisotropy information of human cerebral structu using turbo STEAM diffusion-tensor imaging. Method： Quantitative diffusion anisotropy MR images were obtained in 7 healthy adults using turbo STEAM sequence and a combination of tetrahedral and orthogonal diffusi gradients. Both relative anisotropy(RA) and fractional anisotropy(FA) values were measured various brain regions. The anisotropy index was then compared with the reported valu resulting from EPI-based diffusion tensor imaging.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.138-138
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• 2001

Purpose： To obtain quantitative diffusion-tensor anisotropy information of human cerebral structu using turbo STEAM diffusion-tensor imaging. Method： Quantitative diffusion anisotropy MR images were obtained in 7 healthy adults using turbo STEAM sequence and a combination of tetrahedral and orthogonal diffusi gradients. Both relative anisotropy(RA) and fractional anisotropy(FA) values were measured various brain regions. The anisotropy index was then compared with the reported valu resulting from EPI-based diffusion tensor imaging.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.197-200
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• 2012

Concerning the integrability of almost K$\ddot{a}$hler manifolds, we prove that a compact almost K$\ddot{a}$hler locally symmetric space is K$\ddot{a}$hler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.