• The Pure and Applied Mathematics
• /
• v.28 no.2
• /
• pp.143-153
• /
• 2021

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

• 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］.

• Honam Mathematical Journal
• /
• v.41 no.4
• /
• pp.669-682
• /
• 2019

The objective of this paper is to introduce and study Einstein-like para-Kenmotsu manifolds. For a para-Kenmotsu manifold to be Einstein-like, a necessary and sufficient condition in terms of its curvature tensor is obtained. We also obtain the scalar curvature of an Einstein-like para-Kenmotsu manifold. A necessary and sufficient condition for an almost para-contact metric hypersurface of a locally product Riemannian manifold to be para-Kenmotsu is derived and it is shown that the para-Kenmotsu hypersurface of a locally product Riemannian manifold of almost constant curvature is always Einstein.

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.847-863
• /
• 2020

The aim of the present paper is to study some solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. It is proved that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is gradient Einstein soliton then ${\mu}={\frac{2{\kappa}}{{\kappa}-2}}$. It is shown that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is closed m-quasi Einstein metric then ${\kappa}={\frac{\lambda}{m+2}}$ and 𝜇 = 0. We also study conformal gradient Ricci solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.613-626
• /
• 2021

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1013-1022
• /
• 2018

In this paper, we give a local and global classification of 3-dimensional H-contact manifolds whose Ricci tensor is ${\eta}$-parallel.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1101-1114
• /
• 1996

In Riemannian geometry, it is one of the important things to study the topological or geometric invariants of manifolds since they characterize the topology of manifolds.

• Communications of the Korean Mathematical Society
• /
• v.11 no.2
• /
• pp.463-469
• /
• 1996

We construct closed orientable four-manifolds which have nontrivial Seiberg-Witten invariants, but do not admit any symplectic structure.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.917-934
• /
• 2019

In this paper, we give some classifications of almost Kenmotsu 3-manifolds under homogeneity and some symmetry conditions.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.747-756
• /
• 2003

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.