• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.795-806
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• 2007

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ manifolds with parallel F-traceless component and improve some theorems, provided in the previous paper([2]), which are concerned with the traceless component of the conformal curvature tensor and the spectrum of the Laplacian acting on $p(0{\leq}p{\leq}2)$-forms on the manifold by using the F-traceless component.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.329-338
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• 2012

In this paper, we define the almost h-slant submersion and the h-slant submersion which may be the extended version of the slant submersion [11]. And then we obtain some theorems which come from the slant submersion's cases. Finally, we construct some examples for the almost h-slant submersions and the h-slant submersions.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.963-974
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• 2018

We discuss two kinds of almost contact metric structures on a one-parameter family of totally umbilical hyperspheres in the nearly $K{\ddot{a}}hler$ unit 6-sphere $S^6$.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.147-161
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• 2013

In this paper we determine certain class of $n$-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form, that is, a quaternionic K$\ddot{a}$hler manifold of constant Q-sectional curvature under the conditions (3.1) concerning with the second fundamental form and the induced almost contact 3-structure.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.289-294
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• 2009

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-55
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• 2012

In this paper, we prove that a complex Finsler manifold is a complex locally Minkowski space if and only if it is a strictly K$\ddot{a}$hler-Berwald manifold with zero holomorphic sectional curvature.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.119-128
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• 2013

In the present paper, we define a product-symmetric recurrent-metric connection in an almost Hermitian manifold and study some properties of this connection, in particular, its curvature properties.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1027-1034
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• 2015

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1245-1254
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• 2020

The object of the present paper is to characterize Bach flat (k, 𝜇)-almost co-Kähler manifolds. It is proved that a Bach flat (k, 𝜇)-almost co-Kähler manifold is K-almost co-Kähler manifold under certain restriction on 𝜇 and k. We also characterize (k, 𝜇)-almost co-Kähler manifolds with divergence free Cotton tensor.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.197-210
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• 2020

In this paper, we prove that there are no non-trivial 𝒫ℛ-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds ${\bar{M}}$. We also present a numerical example that illustrates the existence of a 𝒫ℛ-warped product submanifold in ${\bar{M}}$.