• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.999-1006
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• 1997

We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.333-346
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• 1997

The purposer of this paper is to study the spectrum of the Laplacian and the cosymplectic conformal curvature tensor of cosymplectic 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.223-234
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• 2023

The main purpose of this paper is to study the lightlike hypersurface (M, $\overline{g}$) of cosymplectic space form $\overline{M}$(c). In this paper, we computed the Gauss and Codazzi formulae of (M, $\overline{g}$) of cosymplectic manifold ($\overline{M}$, g). We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\overline{M}$(c) with parallel second fundamental form h, parallel screen distribution and c ≠ 0. We showed that if second fundamental form h and local second fundamental form B are parallel, then (M, $\overline{g}$) is totally geodesic. Finally we showed that if (M, $\overline{g}$) is umbilical, then cosymplectic manifold ($\overline{M}$, g) is flat.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.441-447
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• 2002

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

• 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.