• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1749-1771
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• 2014

In this paper, we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifold. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submersions in the cases where the characteristic vector field is vertical or horizontal.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.177-183
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• 2020

The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature -α², provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.

• 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.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.321-327
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• 1999

Graves and Nomizu investigated an indefinite version of the Cartan's result. Specifically they obtained the conditions for all non-degenerate planes to have the same sectional curvature in the in-definite Riemannian manifold. In this paper we are to study the cosym-plective version of the results of Graves and Nomizu and characterize an indefinite cosymplectic spce form.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.87-95
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• 1996

• 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.

• 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.