• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.333-340
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• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• 대한수학회논문집
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• 제18권4호
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• pp.687-693
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• 2003

In this paper, when N is a compact Riemannian manifold, using warped products, we discuss the conformal deformation of a warped product metric on $M\;\;[a,\;\infty)\;\times\;_f\;N$ with specific warping functions.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• 대한수학회보
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• 제56권6호
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• pp.1551-1567
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• 2019

In this paper, Seiberg-Witten-like equations are written down on 3-manifolds. Then, it has been proved that the $L^2$-solutions of these equations are trivial on ${\mathbb{R}}^3$. Finally, a global solution is obtained on the strictly pseudoconvex CR-3 manifolds for a given constant negative scalar curvature.

• 대한수학회보
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• 제59권3호
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• pp.789-799
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• 2022

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.

• 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.

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.333-345
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• 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.

• 충청수학회지
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• 제35권3호
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• pp.235-242
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• 2022

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B × _f² F, where B is a q(> 2)-dimensional base manifold with a nonconstant scalar curvature S_B(x) and F is a 3- dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.

• 대한수학회논문집
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• 제39권2호
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• pp.471-478
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• 2024

The aim of this paper is to investigate some properties of the critical points equations on the statistical manifolds. We obtain some geometric equations on the statistical manifolds which admit critical point equations. We give a relation only between potential function and difference tensor for a CPE metric on the statistical manifolds to be Einstein.

• Advances in aircraft and spacecraft science
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• 제4권6호
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• pp.613-637
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• 2017

The development systems for the Structural Health Monitoring has attracted considerable interest from several engineering fields during the last decades and more specifically in the aerospace one. In fact, the introduction of those systems could allow the transition of the maintenance strategy from a scheduled basis to a condition-based approach providing cost benefits for the companies. The research presented in this paper consists of a definition and next comparison of four methods applied to numerical measurements for the extraction of damage features. The first method is based on the determination of the Structural Intensity field at the on-resonance condition in order to acquire information about the dissipation of vibrational energy throughout the structure. The Damage Quantification Indicator and the Average Integrated Global Amplitude Criterion methods need the evaluation of the Frequency Response Function for a healthy plate and a damaged one. The main difference between these two parameters is their mathematical definition and therefore the accuracy of the scalar values provided as output. The fourth and last method is based on the Mode-shape Curvature, a FRF-based technique which requires the application of particular finite-difference schemes for the derivation of the curvature of the plate. All the methods have been assessed for several damage conditions (the shape, the extension and the intensity of the damage) on two test plates: an isotropic (steel) plate and a 4-plies composite plate.