• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.403-409
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• 1997

Let X be a closed almost complex 4-manifold with $b_2^+(X) > 1$, and have its canonical line bundle as a basic class. Then the pseudo-holomorphic 2-dimensional submanifolds in X with nonnegative self-intersection minimize genus in their homology classes.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.39-45
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• 2016

In this paper, we investigate several properties on a weakly symmetric structure on a Riemannian manifold.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.51-59
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• 2005

Let (M, $g$) be a compact oriented self-dual 4-dimensional Einstein manifold with positive sectional curvature. Then we show that, up to rescaling and isometry, (M, $g$) is $S^4$ or $\mathbb{C}\mathbb{P}_2$, with their cannonical metrics.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.691-697
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• 2004

In this paper we find index form of the multiply warped product manifolds to investigate the physical properties from space-time.

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.629-639
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• 2003

We give results describing behavior of regions of holomorphic extension of CR functions near boundary points of their domain of definition.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1115-1126
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• 2014

The purpose of this paper is to study pointwise slant submersions from almost Hermitian manifolds which extends slant submersion in a natural way. Several basic results in this point of view are proven in this paper.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.803-817
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• 2020

The object of the present paper is to study 𝜂-Ricci soliton on Kenmotsu manifold with respect to general connection.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.771-790
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• 1997

By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in $R^{n + d}, n \geq 2, d \geq 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian n-manifolds into $R^{n + d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the casees of surfaces in $R^3$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.431-440
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• 2013

Let ($M^3$, $g$) be a 3-dimensional closed Sasakian spin manifold. Let $S_{min}$ denote the minimum of the scalar curvature of ($M^3$, $g$). Let ${\lambda}^+_1$ > 0 be the first positive eigenvalue of the Dirac operator of ($M^3$, $g$). We proved in [13] that if ${\lambda}^+_1$ belongs to the interval ${\lambda}^+_1{\in}({\frac{1}{2}},\;{\frac{5}{2}})$, then ${\lambda}^+_1$ satisfies ${\lambda}^+_1{\geq}{\frac{S_{min}+6}{8}}$. In this paper, we remove the restriction "if ${\lambda}^+_1$ belongs to the interval ${\lambda}^+_1{\in}({\frac{1}{2}},\;{\frac{5}{2}})$" and prove $${\lambda}^+_1{\geq}\;\{\frac{S_{min}+6}{8}\;for\;-\frac{3}{2}<S_{min}{\leq}30, \\{\frac{1+\sqrt{2S_{min}}+4}{2}}\;for\;S_{min}{\geq}30$$.