• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.95-110
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• 2008

The object of the present paper is to provide the existence of LP-Sasakian manifolds with $\eta$-recurrent, $\eta$-parallel, $\phi$-recurrent, $\phi$-parallel Ricci tensor with several non-trivial examples. Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.1-10
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• 2022

In the present paper, we have studied conformal Ricci solitons on f-Kenmotsu manifolds of dimension three. Also we have studied 𝜙-Ricci symmetry, 𝜂-parallel Ricci tensor, cyclic parallel Ricci tensor and second order parallel tensor in f-Kenmotsu manifolds of dimension three admitting conformal Ricci solitons. Finally, we give an example.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.303-319
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• 2019

The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.793-805
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• 2017

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying ${\nabla}_{\xi}h=0$, $h{\neq}0$, is ${\eta}$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^2(-4){\times}\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1013-1022
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• 2018

In this paper, we give a local and global classification of 3-dimensional H-contact manifolds whose Ricci tensor is ${\eta}$-parallel.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.705-714
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• 2021

In the present paper, we study 𝜂-Ricci solitons on para-Kenmotsu manifolds with Codazzi type of the Ricci tensor. We study 𝜂-Ricci solitons on para-Kenmotsu manifolds with cyclic parallel Ricci tensor. We also study 𝜂-Ricci solitons on 𝜑-conformally semi-symmetric, 𝜑-Ricci symmetric and conformally Ricci semi-symmetric para-Kenmotsu manifolds. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits 𝜂-Ricci solitons.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.235-244
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• 2006

We shall give a characterization of a real hypersurface M in a complex space form Mn(c), $c\;{\neq}\;0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution of M, and the Ricci operator is ${\eta}-parallel$.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.573-589
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• 2006

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.435-445
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• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.195-202
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• 2007

We prove that a real hypersurface M in a complex space form Mn(c), $c{\neq}0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is ${\eta}-parallel$, is a Hopf hypersurface. We also give a characterization of this hypersurface.