• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.121-136
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• 1996

Met $\tilde{M} = (\tilde{M}, \tilde{J}, <>)$ be an almost Hermitian manifold and M a submanifold of $\tilde{M}$. According to the behavior of the tangent bundle TM with respect to the action of $\tilde{J}$, we have two typical classes of submanifolds. One of them is the class of almost complex submanifolds and another is the class of totally real submanifolds. In 1990, B. Y. Chen [4], [5] introduced the concept of the class of slant submanifolds which involve the above two classes. He used the Wirtinger angle to measure the behavior of TM with respect to the action of $\tilde{J}$.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.619-629
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• 1996

In studying smooth 4-manifolds the Donaldson invariant has played a central role. In [D1] Donaldson showed that non-vanishing Donaldson invariant of a smooth closed oriented 4-manifold X gives rise to the indecomposability of X. For instance, the complex algebraic suface X cannot decompose to a connected sum $X_1 #X_2$ with both $b_2^+(X_i) > 0$.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1047-1065
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• 2017

The notion of a non-metric ${\phi}$-symmetric connection on semi-Riemannian manifolds was introduced by Jin [6, 7]. The object of study in this paper is generic lightlike submanifolds of an indefinite Kaehler manifold ${\bar{M}}$ with a non-metric ${\phi}$-symmetric connection. First, we provide several new results for such generic lightlike submanifolds. Next, we investigate generic lightlike submanifolds of an indefinite complex space form ${\bar{M}}(c)$ with a non-metric ${\phi}$-symmetric connection.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1087-1103
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• 2009

Given a system of s independent 1-forms on a smooth manifold M of dimension m, we study the existence of integral manifolds by means of various generalized versions of the Frobenius theorem. In particular, we present necessary and sufficient conditions for there to exist s'-parameter (s' < s) family of integral manifolds of dimension p := m-s, and a necessary and sufficient condition for there to exist integral manifolds of dimension p', p' $\leq$ p. We also present examples and applications to complex analysis in several variables.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.1
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• pp.7-16
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• 2019

In this paper, for a seismic analysis of an offshore subsea manifold, Response Spectrum Analysis(RSA) and Time History Analysis(THA) were conducted under a various analysis conditions. Response spectrum and seismic design procedure have followed ISO19901-2 code. In case of THA, The response spectrum were converted into artificial earthquake history and both of Explicit and Implicit solvers were used to examine the characteristics of seismic analysis. For the verification, Various seismic analysis methods were applied on a single degree of freedom beam model and a simplified model of the actual manifold. The difference between the results of RSA and THA on the simplified manyfold model evaluated for the analysis of the actual manifold. Because THA is impossible in case of real complex structure such as a manifold, Safety of the actual manifold structure was accessed by using the RSA and the difference between the results of RSA and THA from the simplified model.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.669-670
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• 1994

Let $E \to M$ be a hermitian holomorphic vector bundle over a compact (complex) hermitian manifold M of complex dimension n, and let $$ d"_p(E) : 0 \to A^{p,0}(E) \to A^{p,1}(E) \to \cdots \to A^{p,n}(E) \to 0$$ be the Dolbeault complex. Then $A^{p,q}(E)$ become a prehibert space so that the formal adjoint $\delta"$ of $d"$ and the "Laplacian" $\Delta" = \delta" d" + d" \delta"$ are defined.quot; d" + d" \delta"$ are defined.;$ are defined.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.801-810
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• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.509-536
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• 2010

In this paper, we investigate curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples and is included by that of curvature-adapted and isoparametric submanifolds with flat section. First we introduce the notion of a focal point of non-Euclidean type on the ideal boundary for a submanifold in a Hadamard manifold and give the equivalent condition for a curvature-adapted and complex equifocal submanifold to be proper complex equifocal in terms of this notion. Next we show that the complex Coxeter group associated with a curvature-adapted and proper complex equifocal submanifold is the same type group as one associated with a principal orbit of a Hermann type action and evaluate from above the number of distinct principal curvatures of the submanifold.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1069-1091
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• 2022

We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.