• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.897-904
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• 2022

In this paper, we obtain an inequality involving the squared norm of the covariant differentiation of the shape operator for a real hypersurface in nonflat complex space forms. It is proved that the equality holds for non-Hopf case if and only if the hypersurface is ruled and the equality holds for Hopf case if and only if the hypersurface is of type (A).

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.411-423
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• 2003

Some B.-Y. Chen inequalities for different kind of submanifolds of generalized complex space forms are established.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.271-278
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• 2012

We study some functions defined on the unit tangent space, which are formed with the second fundamental form of submanifolds of a real space form. These give an exact expression of isotropy of submanifolds in a real space form and a relationship between intrinsic invariants and extrinsic ones.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.647-656
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• 2016

In this paper, we define the generalized golden shaped hypersurfaces in Lorentz space forms. Based on the classification of proper semi-Riemannian hypersurfaces in semi-Riemannian real space forms, we obtain the whole families of the generalized golden shaped hypersurfaces in Lorentz space forms.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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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.

• Korean Institute of Interior Design Journal
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• v.22 no.6
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• pp.181-189
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• 2013

Space in the past had characteristics of place which are required for specific behavior to be done as we recognized it easily. However, for space in modern times, the purpose, forms and behavior space has, have changed as tools comprising the space have changed. 'Virtual space' which has been a conversation topic recently is unspecific and changeable space whose forms and geological location are not defined clearly. In addition, behaviors caused by this virtual space in combination with real space are taking place. The nature of Flash Mob which is one of the typical behaviors which take place starting from virtual space to be connected with real space, is that it is intangible game culture whose forms and behaviors are not fixed, and it is not limited to a specific place. Besides, Flash Mob is characteristic of representing game culture in modern society, and its nature can be summarized as temporariness, non-placeness, anonymity, double-sidedness and so forth. Since events generally take place in every place when man is involved in space, it's possible to generally think events derived from interpersonal relationships between man and man. We are to study spatial characteristics of Flash Mob by analyzing features and cases of the Flash Mob by means of them.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.699-708
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• 2004

Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is "Are there any Ricci-parallel real hypersurfaces in complex projective space $P_2C$ or complex hyperbolic space $H_2C$\ulcorner" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.625-638
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• 2013

First we present the explicit formula for the norm of a bilinear form on the 2-dimensional real predual of the Lorentz sequence space $d_*(1,w)^2$. Using this formula, we classify the extreme points of the unit ball of $\mathcal{L}(^2d_*(1,w)^2)$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.189-201
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• 2005

In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.341-347
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• 2014

We classify the exposed symmetric bilinear forms of the unit ball of $\mathcal{L}_s(^2d_*(1,{\omega})^2)$.