• Korean Journal of Mathematics
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• 제29권4호
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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.

• 대한수학회논문집
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• 제38권4호
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• pp.1233-1247
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• 2023

The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.105-116
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• 2018

In this paper, the object is to study a semi-symmetric non-metric connection on an LP-Sasakian manifold whose concircular curvature tensor satisfies certain curvature conditions.

• 대한수학회논문집
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• 제32권4호
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• pp.1033-1045
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• 2017

The conharmonic curvature tensor under certain conditions has been studied for Kenmotsu manifolds with respect to the semi-symmetric metric connection.

• 대한수학회보
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• 제47권5호
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• pp.1089-1103
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• 2010

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

• 대한수학회논문집
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• 제35권3호
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• pp.979-998
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• 2020

We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor 𝓡^(0,2) and also obtain conditions for 𝓡^(0,2) to be symmetric.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.149-156
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• 2015

We analyze the $(LCS)_n$-manifolds endowed with some symmetric properties, focusing on Ricci tensor and the 1-form ${\gamma}$. We study some properties of special Weakly Ricci-Symmetric $(LCS)_n$-manifolds and also shown that Weakly ${\phi}$-Ricci Symmetric $(LCS)_n$-manifold is an ${\eta}$-Einstein manifold.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.9-15
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• 2019

In this paper, we study a type of Riemannian manifold, namely quasi Ricci symmetric manifold. Among others, we show that the scalar curvature of a quasi Ricci symmetric manifold is constant. In addition if the manifold is Einstein, then its Ricci tensor is zero. Also we prove that if the associated vector field of a quasi Ricci symmetric manifold is either recurrent or concurrent, then its Ricci tensor is zero.

• Kyungpook Mathematical Journal
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• 제51권4호
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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.

• 대한수학회논문집
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• 제34권1호
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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.