• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.1-4
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• 2005

In this paper, we will prove that in a compact almost Kahlerian manifold $M^n$, any conformal Killing vector field is Killing if n $\ge$ 4.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.795-803
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• 2014

In this paper, we decompose the curvature tensor (field) on the Abbena-Thurston manifold into three curvature-like tensor fields, and investigate geometric properties.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.707-722
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• 2014

In this paper, we study the forms of the curvatures of lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: M is locally symmetric or M is semi-symmetric.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.821-828
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• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• East Asian mathematical journal
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• v.25 no.4
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• pp.495-504
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• 2009

We introduce three classes of quaternion lightlike submanifolds, screen real lightlike submanifolds and CR lightlike submanifolds of an indefinite quaternion Kaehlerian manifold and study the geometry of leaves of their distributions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.653-665
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• 2009

We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.691-701
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• 2006

In this paper, we construct a new exotic smooth 4-manifold X which is homeomorphic, but not diffeomorphic, to ${\mathbb{C}}\mathbb{P}^2{\sharp}13\overline{\mathbb{C}\mathbb{P}}^2$. Moreover the manifold X has vanishing Seiberg-Witten invariants for all $Spin^c$-structures of X and has no symplectic structure.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.679-692
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• 2006

On a compact oriented n-dimensional manifold $(M^n,\;g)$, it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,\;g)$ is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.689-700
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• 2008

In this paper we prove that a $\phi$-recurrent (k, $\mu$)-contact metric manifold is an $\eta$-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally $\phi$-recurrent (k, $\mu$)-contact metric manifold is the space of constant curvature. The existence of $\phi$-recurrent (k, $\mu$)-manifold is proved by a non-trivial example.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1289-1301
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• 2019

In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.