• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.739-756
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• 2024

The ordinary mean curvature vector field 𝗛 on a submanifold M of a space form is said to be proper if it satisfies equality Δ𝗛 = a𝗛 for a constant real number a. It is proven that every hypersurface of an Riemannian space form with proper mean curvature vector field has constant mean curvature. In this manuscript, we study the Lorentzian hypersurfaces with proper second mean curvature vector field of four dimensional Lorentzian space forms. We show that the scalar curvature of such a hypersurface has to be constant. In addition, as a classification result, we show that each Lorentzian hypersurface of a Lorentzian 4-space form with proper second mean curvature vector field is C-biharmonic, C-1-type or C-null-2-type. Also, we prove that every 𝗛₂-proper Lorentzian hypersurface with constant ordinary mean curvature in a Lorentz 4-space form is 1-minimal.

• Journal of Astronomy and Space Sciences
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• v.19 no.4
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• pp.403-408
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• 2002

3D display of spacecraft motion by using telemetry data received from satellite in real-time is described. Telemetry data are converted to the appropriate form for 3-D display by the real-time preprocessor. Stored playback telemetry data also can be processed for the display. 3D display of spacecraft motion by using real telemetry data provides intuitive comprehension of spacecraft dynamics.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.545-560
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• 1998

Let ø and A be denoted by the structure tensor field of type (1,1) and by the shape operator of a real hypersurface in a complex space form $M_{n}$ (c), c $\neq$ 0 respectively. The main purpose of this paper is to prove that if a real hypersurface in $M_{n}$ (c) satisfies $R_{ξ}$ øA = $AøR_{ξ}$, then the structure vector field ξ is principal, where $R_{ξ}$ / is the Jacobi operator with respect to ξ.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Korean Institute of Interior Design Journal
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• v.14 no.4 s.51
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• pp.19-26
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• 2005

Digital technology continually makes a space evolves. The real-time behavior design communicates the data with the situation of circumference of the space(visitors moving, interior and exterior situations). The space form was changed because it interfaces in real time. The purpose of this study was finding out the characteristics of real-time behavior space design through the analysis of space formative languages, sensorium, S-R and material. This study will be the one of basic references for the digital space design. The boundary of this study set limits to the works of digital space designer who applies the real-time exchanging data to their design among the digital space design works from 1996 to 2004. But it excepted from the real-time behavior space in virtual realty. Therefore, the objects of this study were the works of onl and NOX(paraSITE, Trans-port 2001, Muscle, MotormeCCa, Handdrawspace, Saltwater Pavilion, Son-O-House, H2O Expo). The method was the contents analysis of space formative languages(Greg Lynn's ten space formative languages; bleb, blob, branch, flower, fold, lattice, teeth, shred, skins and strand), sensorium, S-R and material. The results of the study are as follows: 1) The organizational elements; Space formative languages(bleb, blob, fold, shred, skins, strand), stimulation(Human Participation, Human Moving, Weather Conditions), and response(Spatial Moving, Sound Pattern, Lighting Pattern, color Pattern, Activating Particles, Moving Picture, Virtual Friend) 2) The material Use; Sound, lights, and network have been used in the space. Immaterial matter will be used the main material of space design in 21"'century, 3)The spatial types; formal changing of space, projecting immaterial elements, and changing the sound.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.513-532
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• 1999

The purpose of this paper is to give another new characterization of ruled real hypersurfaces in a complex space form $M_n$(c), c$\neq$0 in terms of the covariant derivative of its Weingarten map in the direction of the structure vector $\xi$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.279-294
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• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• East Asian mathematical journal
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• v.37 no.1
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• pp.97-107
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• 2021

Let M be a real hypersurface with almost contact metric structure (��, ξ, ��, g) in a nonflat complex space form Mn(c). We denote S and Rξ by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field ξ respectively. In this paper, we prove that M is a Hopf hypersurface of type (A) in Mn(c) if it satisfies Rξ�� = ��Rξ and at the same time satisfies $({\nabla}_{{\phi}{\nabla}_{\xi}{\xi}}R_{\xi}){\xi}=0$ or Rξ��S = S��Rξ.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.1-15
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• 2010

Let M be a real hypersurface with almost contact metric structure $(\phi,g,\xi,\eta)$ in a complex space form $M_n(c)$, $c\neq0$. In this paper we prove that if $R_{\xi}L_{\xi}g=0$ holds on M, then M is a Hopf hypersurface in $M_n(c)$, where $R_{\xi}$ and $L_{\xi}$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\xi$ respectively. We characterize such Hopf hypersurfaces of $M_n(c)$.

• East Asian mathematical journal
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• v.10 no.2
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• pp.345-358
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• 1994