• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.327-339
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• 2012

In this paper we study $h$-projectively semisymmetric, ${\phi}$-pro-jectively semisymmetric, $h$-Weyl semisymmetric and ${\phi}$-Weyl semisym- metric non-Sasakian ($k$, ${\mu}$)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, ${\mu}$)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.219-228
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• 2019

In this paper it is proved that on an almost $coK{\ddot{a}}hler$ 3-manifold M, (i) M is h-semisymmetric, (ii) the curvature condition $Q{\cdot}R=0$ and (iii) M is $coK{\ddot{a}}hler$ are equivalent.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.261-272
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• 2018

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.539-545
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• 2021

In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

• 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.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.297-306
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• 2012

In this paper we study (${\epsilon}$)-Lorentzian para-Sasakian manifolds and show its existence by an example. Some basic results regarding such manifolds have been deduced. Finally, we study conformally flat and Weyl-semisymmetric (${\epsilon}$)-Lorentzian para-Sasakian manifolds.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.70-81
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• 2024

We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to Eⁿ⁺¹(0) × Sⁿ(4).

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.737-749
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• 2022

We investigate the geometric properties of 𝜂_*-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric 𝜂_*-Ricci soliton on an α-LS manifold is an 𝜂_*-Einstein manifold. Further, we study 𝜑_*-symmetric 𝜂_*-Ricci solitons on such manifolds. We prove that 𝜑_*-Ricci symmetric 𝜂_*-Ricci solitons on an α-LS manifold are also 𝜂_*-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.401-408
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• 2009

The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.