• 대한수학회논문집
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• 제35권1호
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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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• 제63권3호
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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.

• 대한수학회보
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• 제53권4호
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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.

• 대한수학회논문집
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• 제38권3호
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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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• 제24권4호
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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.

• 호남수학학술지
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• 제41권2호
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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.

• 호남수학학술지
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• 제40권2호
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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.

• 대한수학회지
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• 제57권3호
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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.

• 호남수학학술지
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• 제42권1호
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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.

• 한국산업정보학회논문지
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• 제7권3호
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• pp.89-94
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• 2002

본 논문은 주로 개 f-코심플렉틱 다양체를 다룬다. 이 개념은 개 코심플렉틱 다양체와 개 겐모츠 다양체를 포함한다. 개 코심플렉틱 다양체는 ［1］에서 도입된 이래 ［2］, ［3］, ［4］ 등 여러 학자들에 의해 연구되어져 왔으며 개 겐모츠 다양체는 ［5］에서 도입된 이래 ［6］, ［7］ 등에서 연구되어져 왔다. 본 논문에서는 개f-코심플렉틱 다양체의 접촉 초함수에 의해 정의되는 정규 엽층구조의 기하학적 성질을 연구한다. 본 논문의 목적은 ［8］, ［9］에서 얻은 성과를 확장하는 것이다.