• Honam Mathematical Journal
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• v.40 no.2
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• pp.325-346
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• 2018

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)_n$-manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric $(LCS)_3$-manifold whose metric is Ricci soliton.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.685-690
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• 1997

Our study focuses on the condition under which a subspace of complex projective space can become an Einstein space. We prove that a subspace becomes an Einstein space if it's codimension is less than n-1 and its curvature tensor and Ricci tensor satisfies Ryan's condition.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.415-424
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• 2009

The object of the present paper is to study the generalized quasi-Einstein manifolds satisfying some conditions. Finally the existence of such manifolds is ensured by several interesting examples.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.789-799
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• 2009

In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.487-508
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• 2018

In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.855-867
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• 1998

In the present paper, we introduce the notions of quaternionically planar curves and quaternionically projective transformations to the case of almost quaternionic manifold with symmetric affine connection. Also, we obtain an invariant tensor field under the quaternionically projective transformation, and show that a quaternionic Kahlerian manifold with such a vanishing tensor field is of constant Q-sectional curvature.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.215-230
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• 2023

In this article, generalized Sasakian space forms are investigated on W₀ -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W₀-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W₀-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W₀-pseudosymmetry and W₀ -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.327-332
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• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.655-672
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• 2005

The purpose of this paper is to study n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and to give sufficient conditions in order for such a submanifold to be a tube over a quaternionic invariant submanifold.

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.147-154
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• 1981