• Communications of the Korean Mathematical Society
• /
• v.13 no.4
• /
• pp.825-838
• /
• 1998

We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽$_{ξ/}$S = 0 and Sξ = $\sigma$ξ for a smooth function $\sigma$, then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.

• Honam Mathematical Journal
• /
• v.26 no.2
• /
• pp.155-161
• /
• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.157-172
• /
• 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 $M_{n}(C)$.

• Analytical Science and Technology
• /
• v.12 no.6
• /
• pp.1083-1090
• /
• 1999

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.681-694
• /
• 2007

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give some structure theorems for such manifolds.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.28 no.10C
• /
• pp.958-966
• /
• 2003

Change detection algorithms based on frame difference are frequently used for finding moving objects in image sequences. These algorithms detect the change of frames using estimated statistical background model. But, if this estimated background model is different from the actual statistical distribution, false detections are generated. In this paper, we propose an improved change detection algorithm using euler number and structure tensor. The proposed mapping method which is based on the euler number can be used for reducing the false detections that generated by nonparametric change detection algorithm. In this paper, the change in the region of moving object also can be detected by the proposed method using structure tensor. Experimental result shows that the proposed method reduces the false detections effectively by 90% on "Weather", by 34% on "Mother & daughter" and by 43% on "Aisle" than an existing method does.

• East Asian mathematical journal
• /
• v.38 no.5
• /
• pp.549-581
• /
• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c), c≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R_𝜉S = SR_𝜉 and at the same time R_𝜉𝜙 = 𝜙R_𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.133-166
• /
• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.309-339
• /
• 2024

Let M be a real hypersurface in the complex hyperbolic quadric Q^m*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator R_ξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator R_ξ for a real hypersurface M in the complex hyperbolic quadric Q^m*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Q^m* with such a property.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.8 no.8
• /
• pp.2866-2880
• /
• 2014

We propose a video denoising method based on Kalman filter to reduce the noise in video sequences. Firstly, with the strong spatiotemporal correlations of neighboring frames, motion estimation is performed on video frames consisting of previous denoised frames and current noisy frame based on intensity and structure tensor. The current noisy frame is processed in temporal domain by using motion estimation result as the parameter in the Kalman filter, while it is also processed in spatial domain using the Wiener filter. Finally, by weighting the denoised frames from the Kalman and the Wiener filtering, a satisfactory result can be obtained. Experimental results show that the performance of our proposed method is competitive when compared with state-of-the-art video denoising algorithms based on both peak signal-to-noise-ratio and structural similarity evaluations.