• 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.

• 대한수학회지
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• 제16권1호
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• pp.71-85
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• 1979

• 충청수학회지
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• 제8권1호
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• pp.131-136
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• 1995

We give another detailed proof of the existence of a holomorphic structure on a smooth complex vector bundle over a complex manifold.

• East Asian mathematical journal
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• 제35권5호
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• pp.529-534
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• 2019

The purpose of this article is to present The $Carath{\acute{e}}odory$-Cartan-Kaup-Wu theorem for connected Kobayashi hyperbolic almost complex manifolds.

• 대한수학회지
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• 제39권2호
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• pp.253-275
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• 2002

The purpose of this paper is to study complete complex submanifolds of a locally symmetric Kaehler manifold with non-positive totally real normal bisectional curvature and k-pinched totally real tangent bisectional curvature.

• 대한수학회지
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• 제45권2호
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• pp.367-376
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• 2008

The main purpose of this paper is to investigate diagonal lift of tensor fields of type (1,1) from manifold to its tensor bundle of type (p, q) and to prove that when a manifold $M_n$ admits a $K\ddot{a}hlerian$ structure ($\varphi$,g), its tensor bundle of type (p,q) admits an complex structure.

• 대한수학회논문집
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• 제27권2호
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• pp.307-315
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• 2012

We study the geometry of real lightlike hypersurfaces of an inde nite Kaehler manifold $\bar{M}$. We provide new results on such a real lightlike hypersurface $M$ by using the $F$-structure of $M$ induced by the almost complex structure $J$ of $\bar{M}$.

• 대한수학회논문집
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• 제35권2호
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• pp.591-602
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• 2020

There is a well-known class of compact, complex, non-Kählerian manifolds constructed by Bosio, called the LVMB manifolds, which properly includes the Hopf manifold, the Calabi-Eckmann manifold, and the LVM manifolds. As in the case of LVM manifolds, these LVMB manifolds can admit a regular holomorphic foliation 𝓕. Moreover, later Meersseman showed that if an LVMB manifold is actually an LVM manifold, then the regular holomorphic foliation 𝓕 is actually transverse Kähler. The aim of this paper is to deal with a converse question and to give a simple and new proof of a well-known result of Cupit-Foutou and Zaffran. That is, we show that, when the holomorphic foliation 𝓕 on an LVMB manifold N is transverse Kähler with respect to a basic and transverse Kähler form and the leaf space N/𝓕 is an orbifold, N/𝓕 is projective, and thus N is actually an LVM manifold.

• East Asian mathematical journal
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• 제16권1호
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• pp.135-145
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• 2000

The purpose of this paper is to study the Chern-type problem of the complete space-like submanifolds of an indefinite complex space form.

• 대한수학회논문집
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• 제26권4호
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• pp.635-647
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• 2011

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of $\bar{M}$.