• 대한수학회보
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• 제48권6호
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• 동의생리병리학회지
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• 제20권4호
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• pp.784-792
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• 2006

The Neo-Confucian study of the thee of ministerial fire(相火論) constitute of the rule of iung jung(中正), the principal of form and use(體用) and of real nature and emotion(性情) of human and ethic mind(人心道心). The present study is to evaluate a fundamental concept of the theory of ministerial fire, which is one of traditional medical ideology in China, through the Neo-Confucianism projects to The theory of ministerial fire. The theory of ministerial fire of Judange(朱丹溪) was recognized by ontological principal of Heaven-Human being-Earth, ontological structure of Form-Use and the structure that mind consist of real nature and emotion(심統性惰). The ethic and human mind(道心人心) of Judange and constancy and transition(常變) of seven emotion have relationship in the ontological structure of Form-Use. The real nature of human Doing consisted of apriority of Heaven rule is unitary constructed by Form-Use(체용) of inactivated real nature and activated seven emotion and then activated seven emotion shows dual form of appropriate(中節) and inappropriate(不中節). Emperor's and ministerial fire(君火相火) which has a relationships of Heaven-Human being synchronization represents all kinds of fire and classified to heaven fire(天火) and human fire(人火). The emperor's fire was triggered by inactivated fire and ministerial fire(相火) was triggered by activated fire. Inactivated ministerial fires have dual form of physiological ministerial and pathological ministerial fire. Regarding the forementioned analytic thinking, it was clear that manifest processing of One's real nature and the ministerial fire undergo the same principal and logics. Since maintained One's real nature that is inactivated seven emotion and appropriated activated seven emotion, ministerial fire can be stable and keep one's health and well-being in mind and body.

• 호남수학학술지
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• 제26권2호
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• pp.155-161
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• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.557-564
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• 2001

The objective of he study is to record the real conditions along with the soccer ball that is, each player's ball keeping time, the number football keeping, accuracy of passing to other player, direction, etc., on a real-time basis, measure them in numbers and get necessary analyzed output as much as one needs. The study consists of the following stages: (1) Record the data by drawing through Visual Interface on a real-time basis; (2) Graphic windows to display the recorded data item by item in graphic; (3) Form windows to display the individual or team scores anytime when needed; (4) Windows to display the analyzed data in visualized form. The effect of the study is threefold: (1) It inputs all the game-related data on a real-time basis, which was impossible before and shows analyzed contents during the game enabling each tea manager o use; (2) In cse of TV broadcasting or newspaper articles, it explains objectively the situations of he game to the TV viewers or readers; (3) After the game, it provides importance information on each team's playing ability and individual player's technical improvement through data analysis.

• 대한수학회지
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• 제47권5호
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• pp.1001-1015
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• 2010

Let M be a $C^{\infty}$ real hypersurface in $\mathbb{C}^{n+1}$, $n\;{\geq}\;1$, locally given as the zero locus of a $C^{\infty}$ real valued function r that is defined on a neighborhood of the reference point $P\;{\in}\;M$. For each k = 1,..., n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n - k at P. The problem is to find an integral manifold of the real 1-form $i{\partial}r$ on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.

• 호남수학학술지
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• 제28권4호
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• pp.573-589
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• 2006

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.

• 대한수학회보
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• 제26권2호
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• pp.159-164
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• 1989

Let M be a hypersurface of dimension n(.geq.2) in an (n+1)-dimensional real space form over bar M(c) with constant curvature c and H the second fundamental tensor of M. M is said to be birecurrent if here exists a covariant tensor field .alpha. of order 2 such that .del.$^{2}$H=H .alpha., where .del. is the connection of M. Also, M is said to be recurrent if there exists a 1-form .betha. such that .del.H=H .betha.. Matsuyama [2] recently proved that a recurrent hypersurface M in a real space form is locally symmetric and a complete irreducible birecurrent hypersurface M in a real space form is recurrent. The main purpose of this paper is to characterize the birecurrent or recurrent hypersurface M of a Riemannian manifold with constant curvature c and to prove that M is classified as a cylinder, $M^{n}$ (c) or ( $c_{1}$)* $M^{n-r}$ ( $c_{2}$) where 1/ $c_{1}$+1/ $c_{2}$=1/c.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1207-1235
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• 2016

Let M be a real hypersurface with constant mean curvature in a complex space form $M_n(c),c{\neq}0$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ with respect to the structure vector field ${\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor field ${\phi}$, then M is a homogeneous real hypersurface of Type A.

• 대한수학회지
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• 제41권5호
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.541-575
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• 2016

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor ${\phi}$, then M is a homogeneous real hypersurface of Type A provided that $TrR_{\xi}$ is constant.