• 호남수학학술지
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• 제41권4호
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• pp.769-780
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• 2019

We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.

• 대한수학회보
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• 제37권1호
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• pp.85-90
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• 2000

On Riemannian manifolds of dimension 4 the Einstein condition is equivalent to the Thorpe condition. In this paper, we construct a few metrics which we Einstein but not Thorpe, and vice versa in dimensions larger than 4.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.737-749
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• 2022

We investigate the geometric properties of 𝜂_*-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric 𝜂_*-Ricci soliton on an α-LS manifold is an 𝜂_*-Einstein manifold. Further, we study 𝜑_*-symmetric 𝜂_*-Ricci solitons on such manifolds. We prove that 𝜑_*-Ricci symmetric 𝜂_*-Ricci solitons on an α-LS manifold are also 𝜂_*-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.623-638
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• 2023

In this article we study a 𝛿-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study 𝛿-Ricci-Yamabe almost soliton and gradient 𝛿-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a 𝛿-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to 𝜉, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gradient 𝛿-Ricci-Yamabe almost soliton. We demonstrate a 𝛿-Ricci-Yamabe almost soliton on a (𝜅, 𝜇)-paracontact manifold.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.361-375
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• 2018

The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

• 호남수학학술지
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• 제46권1호
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• pp.70-81
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• 2024

We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to Eⁿ⁺¹(0) × Sⁿ(4).

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.781-790
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• 2021

The goal of this paper is to characterize a class of almost Kenmotsu manifolds admitting *-conformal Ricci solitons. It is shown that if a (2n + 1)-dimensional (k, µ)'-almost Kenmotsu manifold M admits *-conformal Ricci soliton, then the manifold M is *-Ricci flat and locally isometric to ℍⁿ⁺¹(-4) × ℝⁿ. The result is also verified by an example.

• 대한수학회지
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• 제58권5호
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• pp.1081-1107
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• 2021

In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study their structure, and in particular completely classify smooth toric special weak Fano 4-folds. As a result, we can confirm that almost every smooth toric special weak Fano 4-fold is a weakened Fano manifold, that is, a weak Fano manifold which can be deformed to a Fano manifold.

• 대한수학회보
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• 제37권4호
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• pp.721-727
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• 2000

We study some spectral properties of the $\rho-Laplacian$ on quaternionic Kaehler manifolds.

• 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.