• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.285-294
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• 2013

The present paper deals with a study of ${\phi}$-pseudo symmetric and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifolds. It is shown that every ${\phi}$-pseudo symmetric $(LCS)_n$-manifold and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifold are ${\eta}$-Einstein manifold.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.507-520
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• 2009

The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.177-186
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• 2017

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.517-523
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• 2017

The purpose of the present paper is to study an almost generalized pseudo-Ricci symmetric manifold. The existence of such manifold is ensured by an example. Furthermore, having found, faulty example in [13], the present paper also attempts to construct a non-trivial example of an almost pseudo Ricci symmetric manifold.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.921-934
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• 2019

The object of the present paper is to study generalized pseudo-projectively symmetric manifolds and Einstein generalized pseudo-projectively symmetric manifolds. Finally, the existence of generalized pseudo-projectively symmetric manifolds have been proved by two non-trivial examples.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.457-468
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• 2011

We consider pseudo-symmetric and Ricci generalized pseudo-symmetric N(${\kappa}$) contact metric manifolds. We also consider N(${\kappa}$)-contact metric manifolds satisfying the condition $S{\cdot}R$ = 0 where R and S denote the curvature tensor and the Ricci tensor respectively. Finally we give some examples.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.39-45
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• 2016

In this paper, we investigate several properties on a weakly symmetric structure on a Riemannian manifold.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.615-621
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• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.731-739
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• 2015

The object of the present paper is to characterize a Riemannian manifold admitting a type of semi-symmetric non-metric connection.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.829-841
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• 2020

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.