• 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.

• 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.865-874
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• 2004

The present paper treats with a subfoliation of a CR-foliation F on an almost Hermitian manifold M. When M is locally conformal almost Kahler, it has three OR-foliations. We show that a CR-foliation F on such manifold M admits a canonical subfoliation D(1/ F) defined by its totally real subbundle. Furthermore, we investigate some cohomology classes for D(1/ F). Finally, we construct a new one from an old locally conformal almost K hler (in particular, an almost generalized Hopf) manifold.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.109-114
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• 2001

Using Fermi coordinate and Jacobi operator on Kahler manifold, we characterize partially conformal geodesic transformation in Kahler geometry.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.515-519
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• 2003

Let M be a hyperkahler manifold with the hyperkahler structure (g, I, J, K). In [5], D. Huybrechts suggests that it is an open and interesting question whether any Kahler class that stays Kahler in the twister family can actually be represented by an harmonic Kahler form. In this paper we will consider both this problem and the set of all the primitive harmonic Kahler forms on M.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.185-189
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• 1973

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.303-315
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• 2001

In this paper, we investigate the topology of complex Finsler manifolds. For a complex Finsler manifold (M, F), we introduce a certain condition on the Finsler metric F on M. This is a generalization of Kahler condition for the Hermitian metric. Under this condition, we can produce a Kahler metric on M. This enables us to use the usual techniques in the Kahler and Riemannian geometry. We show that if the holomorphic sectional curvature of $ M is\geqC^2>0\; for\; some\; c>o,\; then\; diam(M)\leq\frac{\pi}{c}$ and hence M is compact. This is a generalization of the Bonnet\`s theorem in the Riemannian geometry.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.757-766
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• 2007

In this note we construct an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non-$K\ddot{a}hler$, symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.507-519
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• 2023

The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'^*_g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S¹. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

• Kyungpook Mathematical Journal
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• v.14 no.1
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• pp.7-14
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• 1974