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

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.257-273
• /
• 2020

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.553-562
• /
• 1995

In a Recent paper [3], D. Chinea, M. Delon and J. C. Marrero proved that a cosymplectic manifold is formal and constructed an example of compact cosymplectic manifold which is not a global product of a Kaehler manifold with the circle. In this paper we study the compact cosymplectic manifolds with critical Riemannian metrics.

• Kyungpook Mathematical Journal
• /
• v.63 no.3
• /
• pp.507-519
• /
• 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
• /
• v.54 no.1
• /
• pp.85-97
• /
• 2017

We classify Kenmotsu 3-manifolds and cosymplectic 3-manifolds with ${\eta}-parallel$ Ricci operator.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1749-1771
• /
• 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
• /
• v.60 no.1
• /
• pp.177-183
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.62 no.2
• /
• pp.333-345
• /
• 2022

We study *-Ricci solitons on non-cosymplectic (κ, µ)-acs (almost cosymplectic) manifolds M. We find *-solitons that are steady, and such that both the scalar curvature and the divergence of the potential field is negative. Further, we study concurrent, concircular, torse forming and torqued vector fields on M admitting Ricci and *-Ricci solitons. Also, we provide some examples.

• Honam Mathematical Journal
• /
• v.44 no.2
• /
• pp.231-243
• /
• 2022

In the present paper we study the properties of α-cosymplectic manifolds endowed with *-conformal η-Ricci solitons and gradient *-conformal η-Ricci solitons.

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