• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.507-519
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• 2023

The aim of this paper is to study the Fisher-Marsden conjucture in the frame work of f-cosymplectic and (k, µ)-cosymplectic manifolds. First we prove that a compact f-cosymplectic manifold satisfying the Fisher-Marsden equation R'^*_g = 0 is either Einstein manifold or locally product of Kahler manifold and an interval or unit circle S¹. Further we obtain that in almost (k, µ)-cosymplectic manifold with k < 0, the Fisher-Marsden equation has a trivial solution.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1249-1257
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• 2016

We prove that the Ricci operator S of an almost cosymplectic three-manifold M is invariant along the Reeb flow, that is, M satisfies ${\pounds}_{\xi}S=0$ if and only if M is either cosymplectic or locally isometric to the group E(1, 1) of rigid motions of Minkowski 2-space with a left invariant almost cosymplectic structure.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.881-892
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• 2023

In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on (κ, µ)-almost cosymplectic manifold M with κ < 0 and we show that the soliton is expanding with ${\lambda}{\frac{\kappa}{2n-1}}(4n - 1)$ and M is locally isometric to the Lie group G_ρ. Finally, we prove the non-existence of gradient almost Riemann soliton on a (κ, µ)-almost cosymplectic manifold of dimension greater than 3 with κ < 0.

• East Asian mathematical journal
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• v.24 no.4
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• pp.421-429
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• 2008

We study invariant lightlike submanifolds and almost contact CR-lightlike submanifolds of an indefinite cosymplectic manifold.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.269-284
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• 2019

The object of the paper is to investigate almost alpha-cosymplectic (${\kappa},{\mu},{\nu}$) spaces. Some results on almost alpha-cosymplectic (${\kappa},{\mu},{\nu}$) spaces with certain conditions are obtained. Finally, we give an example on 3-dimensional case.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.293-304
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• 2018

In this paper, we study ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space and prove that it is an ${\eta}$-Einstein manifold with constant coefficients. Next, we show that a three-dimensional locally ${\varphi}$-recurrent almost cosymplectic (${\kappa},{\mu}$)-space is the space of constant curvature.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.175-185
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• 2020

In this paper, we introduce almost α-Cosymplectic f-manifolds endowed with a semi-symmetric non-metric connection and give some general results concerning the curvature of such connection. In particular, we study some curvature properties of an almost α-cosymplectic f-manifold equipped with semi-symmetric non-metric connection.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.3
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• pp.89-94
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• 2002

The present paper mainly treats with almost f-cosymplectic manifolds. This notion contains almost cosymplectic and almost Kenmotsu manifolds. Almost cosymplectic manifolds introduced in ［1］ have been studied by many schalors, say ［2］, ［3］, ［4］, and almost Kenmotsu manifolds introduced in ［5］ have been studied in ［6］, ［7］. The present paper studies some geometrical and topological properties of the canonical foliation defined by the contact distribution of an almost f-cosymplectic manifold. The purpose of the present paper is to extend the results obtained in ［8］, ［9］.