• 호남수학학술지
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• 제30권3호
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• pp.535-550
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• 2008

Let M be a real hypersurface of a complex space form with almost contact metric structure $({\phi},{\xi},{\eta},g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

• 대한수학회지
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• 제43권5호
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Structural Engineering and Mechanics
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• 제41권5호
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• pp.663-673
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• 2012

A number of mode shape-based structure damage identification methods have been verified by numerical simulations or experiments for on-line structure health monitoring (SHM). However, many of them need a baseline mode shape generated by the healthy structure serving as a reference to identify damages. Otherwise these methods can hardly perform well when multiple cracks conditions occur. So it is important to solve the problems above. By aid of the fractal dimension method (FD), Qiao and Wang proposed a generalized fractal dimension (GFD) to detect the delamination damage. As a modification of GFD, Qiao and Cao proposed the approximate waveform capacity dimension (AWCD) technique to simplify the calculation of fractal and overcome the false peak appearing in the high mode shapes. Based on their valued work, this paper combined and applied the AWCD method and curvature mode shape data to detect multiple damages in beam. In the end, the identification properties of the AWCD for multiple damages have been verified by groups of Monte Carlo simulations and experiments.

• 호남수학학술지
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• 제36권4호
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• pp.805-812
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• 2014

For unit tangent sphere bundles $T_1M$ with the standard contact metric structure (${\eta},\bar{g},{\phi},{\xi}$), we have two fundamental operators that is, $h=\frac{1}{2}{\pounds}_{\xi}{\phi}$ and ${\ell}=\bar{R}({\cdot},{\xi}){\xi}$, where ${\pounds}_{\xi}$ denotes Lie differentiation for the Reeb vector field ${\xi}$ and $\bar{R}$ denotes the Riemmannian curvature tensor of $T_1M$. In this paper, we study the Reeb ow invariancy of the corresponding (0, 2)-tensor fields H and L of h and ${\ell}$, respectively.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회(1)
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• pp.581-582
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• 2005

• 대한수학회보
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• 제42권2호
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• pp.337-358
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• 2005

Let M be a real hypersurface with almost contact metric structure $(\phi,\;\xi,\;\eta,\;g)$ in a nonflat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ commutes with both the structure tensor $\phi$ and the Ricc tensor S, then M is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of M is constant or $g(S\xi,\;\xi)$ is constant.

• 대한수학회보
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• 제44권1호
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• pp.157-172
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• 2007

In this paper, we prove that if the structure Jacobi operator $R_{\xi}-parallel\;and\;R_{\xi}$ commutes with the Ricci tensor S, then a real hypersurface with non-negative scalar curvature of a nonflat complex space form $M_{n}(C)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_{n}(C)$.

• 대한수학회논문집
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• 제39권1호
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• pp.161-173
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• 2024

The main object of the present paper is to study conformal Ricci soliton on paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection satisfying the condition $^*_C({\xi},U){\cdot}^*_S=0$. Finally we characterized concircular curvature tensor on paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection.

• 대한수학회지
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• 제57권4호
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• pp.1005-1018
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• 2020

A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹ⁿ(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.