• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1361-1371
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• 2017

In this paper, we introduce a framework of (${\alpha},{\beta}$)-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.53-68
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• 2017

The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.279-294
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• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1035-1047
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• 2004

In this paper, we study the unit tangent sphere bundles T$_1$M(4c) of complex space forms M(4c) with constant holomorphic sectional curvature 4c. In particular, we determine T$_1$M(4c) whose Ricci tensors satisfy the Einstein-like conditions.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1285-1303
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• 2018

This note is motivated by gradient estimates of Li-Yau, Hamilton, and Souplet-Zhang for heat equations. In this paper, our aim is to investigate Yamabe equations and a non linear heat equation arising from gradient Ricci soliton. We will apply Bochner technique and maximal principle to derive gradient estimates of the general non-linear heat equation on Riemannian manifolds. As their consequence, we give several applications to study heat equation and Yamabe equation such as Harnack type inequalities, gradient estimates, Liouville type results.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1103-1129
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• 2018

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

• The Pure and Applied Mathematics
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• v.9 no.2
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• pp.107-111
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• 2002

In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if $\phi$ : $M\;\longrightarrow\;N$ is a quasi-strongly p-harmonic map (\rho\; $\geq\;2$) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the $(2\rho－2)$-energy, $E_{2p-2}(\phi)$ is finite, then $\phi$ is constant.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.149-164
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• 2021

By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.763-774
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• 2023

If a paraSasakian manifold of dimension (2n + 1) represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric g has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if r = -6; shrinking if r > -6; expanding if r < -6.

• Advances in aircraft and spacecraft science
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• v.4 no.6
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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.