• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.953-963
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• 2008

We find necessary and sufficient conditions for a para-$K{\ddot{a}}hlerian$ manifold to be paraholomorphically pseudosymmetric in terms of the paraholomorphic projective and Bochner curvatures. New examples of such spaces are proposed.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.789-798
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• 2018

Let M be a compact almost $coK{\ddot{a}}hler$ 5-manifold with $K{\ddot{a}}hlerian$ leaves. In this paper, we prove that M is locally symmetric if and only if it is locally isometric to a Riemannian product of a unit circle $S^1$ and a locally symmetric compact $K{\ddot{a}}hler$ 4-manifold.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.199-206
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• 2013

We present a 4-dimensional nil-manifold as the first example of a closed non-K$\ddot{a}$hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K$\ddot{a}$hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1061-1075
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• 2019

In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.