• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.369-383
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• 1994

A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of 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.(omitted)

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.433-442
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• 2008

In this paper we consider a real hypersurface M in complex hyperbolic space $H_n\mathbb{C}$ satisfying $S{\phi}A\;=\;{\phi}AS$, where $\phi$, A and S denote the structure tensor, the shape operator and the Ricci tensor of M respectively. Moreover, we give a characterization of real hypersurfaces of type A in $H_n\mathbb{C}$ by such a commuting Ricci tensor.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.399-410
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• 2016

In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.535-550
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• 2008

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 ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.227-243
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• 1988

• East Asian mathematical journal
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• v.13 no.1
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• pp.11-22
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• 1997