• 대한수학회보
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• 제52권1호
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• pp.335-344
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• 2015

We characterize a homogeneous real hypersurface of type (A) or a ruled real hypersurface in a non-flat complex space form, respectively.

• 대한수학회보
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• 제47권2호
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• pp.341-353
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• 2010

In this paper, we study the geometry of screen conformal lightlike real hypersurfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for screen conformal lightlike real hypersurfaces of an indefinite complex space form.

• 대한수학회지
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• 제55권3호
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• pp.735-747
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• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• 대한수학회보
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• 제26권1호
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• pp.69-74
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• 1989

Recently one of the present authors [2] asserted that a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of cyclic parallel if and only if AJ=JA and he showed also a complete and connected cyclic-parallel real hypersurface of M$^{n}$ (c), is congruent to type $A_{1}$, $A_{2}$ or A according as c>0 or c<0. A real hypersurface of a complex space form M$^{n}$ (c) is said to be covariantly cyclic constant if the cyclic sum of covariant derivative of the second fundamental form is constant. The purpose of the present paper is to extend theorem 3 and 4 in [2] when the hypersurfaces are of coveriantly cyclic constant, that is a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of covariantly cyclic constant if an only if AJ=JA, and a complete and connected covariantly cyclic constant real hypersurface of M$^{n}$ (c) is congruent to type $A_{1}$, $A_{2}$ or a according as c>0 or c<0.

• 대한수학회지
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• 제46권1호
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• 대한수학회지
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• 제33권1호
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• pp.101-119
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• 1996

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$.

• 대한수학회보
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• 제34권2호
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• pp.173-184
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• 1997

An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

• 대한수학회지
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• 제46권5호
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• pp.979-995
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• 2009

As warped product manifolds provide an excellent setting to model space time near black holes or bodies with large gravitational field, the study of these manifolds assumes significance in general. B. Y. Chen [4] initiated the study of CR-warped product submanifolds in a Kaehler manifold. He obtained a characterization for a CR-submanifold to be locally a CR-warped product and an estimate for the squared norm of the second fundamental form of CR-warped products in a complex space form (cf [6]). In the present paper, we have obtained a necessary and sufficient conditions in terms of the canonical structures P and F on a CR-submanifold of a nearly Kaehler manifold under which the submanifold reduces to a locally CR-warped product submanifold. Moreover, an estimate for the second fundamental form of the submanifold in a generalized complex space is obtained and thus extend the results of Chen to a more general setting.

• 한국실내디자인학회논문집
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• 제20권5호
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• pp.51-58
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• 2011

As it gets nearer to the modern society, social and cultural situations are changing and the spatial form of public space is changing into the complex structure where it is interlinked with each other diversely. In particular, as the development of large-scale complex spreads nationwide, the form of complex commercial space assuming the nature of malls appears prominently. In such a large-scale complex commercial space, the diverse visual elements make the environment difficult to be perceived. Like this, the attention in the commercial space where a variety of visual stimuli are in the presence, is important element, so the plan of VP(visual presentation) is needed for effectively selecting or inducing the space. Thus, in this study, human visual and perception process will be reviewed and a method to evaluate the attention will be proposed. Also, the attention of each stores in the complex commercial spaces will be evaluated to propose the indicators for resonable spatial panning in the future.

• 호남수학학술지
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• 제32권4호
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• pp.747-761
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• 2010

It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{\xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{\xi}$ which are weaker than ${\nabla}R_{\xi}$ = 0. Under further condition $S\phi={\phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.