• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.145-149
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• 2006

We demonstrate a novel almost Kahler deformation on $\mathbb{R}^4$ which diffuses the scalar curvature.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.405-413
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• 2005

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.809-820
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• 2004

On $R^{2n}$, n$\geq$2, with the standard symplectic structure we construct compatible almost K hler metrics with negative scalar curvature on a polydisc which are Euclidean away from the polydisc.c.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1015-1029
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• 2003

In this paper, we study a connected, simply connected homogeneous Kahler surface with distinct constant Ricci eigenvalues, and specify the local structure of them.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.384-390
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• 2022

In this paper, we study the obstruction on the jets of an almost complex structure J to the existence of a symplectic form ω such that J is compatible with ω. We describe some almost complex structures on ℝ⁴ and on ℝ⁶, respectively, that cannot be calibrated by any symplectic forms. In particular, these examples pertain to the model almost complex structure on ℝ⁴ in [3], and the simple model structure on ℝ⁶ in [7].

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1501-1511
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• 2021

In this paper we study magnetic trajectories on ℍ³ × ℝ with respect to the strictly almost Kähler structure. We find three types of magnetic curves which correspond to the almost complex structure compatible to the product metric on ℍ³ × ℝ.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.167-178
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• 2010

We discuss the critical points of the functional $F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g$ on the spaces of all almost Hermitian structures AH(M) with $(\lambda,\mu){\in}R^2-(0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $F_{\lambda,\mu}(J,g)$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.237-243
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• 1992

Let (M, g, J) be a closed Kahler manifold of complex dimension m > 1. We denote by Spec(M,g) the spectrum of the real Laplace-Beltrami operator. DELTA. acting on functions on M. The following characterization problem on the spectral rigidity of the complex projective space (CP$^{m}$ , g$_{0}$ , J$_{0}$ ) with the standard complex structure J$_{0}$ and the Fubini-Study metric g$_{0}$ has been attacked by many mathematicians : if (M,g,J) and (CP$^{m}$ ,g$_{0}$ ,J$_{0}$ ) are isospectral then is it true that (M,g,J) is holomorphically isometric to (CP$^{m}$ ,g$_{0}$ ,J$_{0}$ )\ulcorner In [BGM], [LB], it is proved that if (M,J) is (CP$^{m}$ , J$_{0}$ ) then the answer to the problem is affirmative. Tanno ([Ta]) has proved that the answer is affirmative if m .leq. 6. Recently, Wu([Wu]) has showed in a more general sense that if (M, g) and (CP$^{m}$ ,g$_{0}$ ) are (-4/m)-isospectral, m .geq. 4, and if the second betti number b$_{2}$(M) is equal to b$_{2}$(CP$^{m}$ ).