• 대한수학회보
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• 제21권2호
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• pp.61-66
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• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• 호남수학학술지
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• 제44권1호
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.847-863
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• 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.

• 대한수학회지
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• 제47권3호
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• pp.505-521
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• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• 대한수학회보
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• 제52권3호
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• pp.1027-1034
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• 2015

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.

• 대한수학회보
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• 제53권4호
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• pp.1237-1247
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• 2016

The object of the present paper is to characterize $({\kappa}$, ${\mu}$)-contact metric manifolds whose concircular curvature tensor satisfies certain semisymmetry conditions. We also verify that the result holds by a concrete example.

• 대한수학회논문집
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• 제37권4호
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• pp.1209-1219
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• 2022

The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.535-549
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• 2020

In this paper, we introduce the geometry of contact CR submanifolds and radical transversal lightlike submanifolds of Sasaki-like almost contact manifolds with B-metric. We obtain some new results that establish a relationship between these two submanifolds.

• 대한수학회논문집
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• 제35권2호
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• pp.639-651
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• 2020

Consider a gradient Einstein-type metric in the setting of K-contact manifolds and (κ, µ)-contact manifolds. First, it is proved that, if a complete K-contact manifold admits a gradient Einstein-type metric, then M is compact, Einstein, Sasakian and isometric to the unit sphere 𝕊²ⁿ⁺¹. Next, it is proved that, if a non-Sasakian (κ, µ)-contact manifolds admits a gradient Einstein-type metric, then it is flat in dimension 3, and for higher dimension, M is locally isometric to the product of a Euclidean space 𝔼ⁿ⁺¹ and a sphere 𝕊ⁿ(4) of constant curvature +4.