• 대한수학회지
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• 제61권2호
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• pp.309-339
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• 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.

• 헤리티지:역사와 과학
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• 제52권4호
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• pp.264-271
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• 2019

별을 관측하는 천문대로 잘 알려진 경주 첨성대는 그 모양과 성격이 독특하고 원래의 모습으로 잘 보존되어 있어 역사적·학술적·예술적 가치가 높은 문화재이다. 그동안 많은 연구자들이 첨성대의 외부 구조와 지반 안전성, 지진 재해 위험도 평가 연구 등 과학적인 조사를 이용한 첨성대의 평가를 진행해왔으나 첨성대의 지하 구조에 대해서는 조사가 매우 미흡하였다. 이 논문에서는 첨성대와 관련한 주변의 매장문화재 존재 여부와 첨성대의 기초부를 확인하기 위하여 지하투과레이더(GPR) 탐사를 수행하고 2차원과 3차원 영상을 통해 첨성대의 지하 구조를 정밀 분석하였다. 그 결과, 0.4~0.6m 깊이에서는 절반 정도만 남아 있긴 하지만 12개의 작은 물체들이 원형의 배치를 이루고 있고, 0.7~1m 깊이에서는 정면 4칸, 측면 3칸의 건물지로 추정되는 반응이 첨성대를 중심으로 주변에 분포하는 것이 확인되었다. 또한 첨성대의 직하부에는 이미 알고 있는 2단의 기단부 외에 7×7m 크기의 방형 시설이 깊이 0.6m에 존재하며, 깊이 1.2~3m에서는 첨성대의 기초시설로 추정되는 반응이 확인되었다. 이 기초시설은 동서 11m, 남북 12m의 타원형이며 첨성대 기단을 중심으로 북·서·동측면은 1m 이내로 짧고 남측면은 5m 정도로 넓게 분포하고 있다.

• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.

• East Asian mathematical journal
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• 제36권3호
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• pp.389-415
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• 2020

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, ξ, η, g) in a complex space form M_n+1(c), c ≠ 0. We denote by R_ξ and R'_X be the structure Jacobi operator with respect to the structure vector ξ and be R'_X = (∇_XR)(·, X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a 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 R'_ξ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature ${\bar{r}}$ of M holds ${\bar{r}}-2(n-1)c{\leq}0$.

• 한국표면공학회지
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• 제33권1호
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• pp.25-33
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• 2000

The synthesis and characterization of intercalated compound of dodecanesulfornate into hydrated metal, [M($H_2$O)\ulcorner](C\ulcornerH\ulcorner$SO_3$)$_2$.$xH_2$O (M=Co, Cu) was presented. The compounds shows a layered structure which was determined by powder X-ray diffraction. Thermal behavior of the layered structure was investigated using thermal analysis, and FT-IR spectroscopy by varying the temperature. The increase in layer spacing of the products by increasing the temperature is also checked by X-ray diffraction. We can suggest three kinds of layered structure by varying the temperature, which is accompanied by changing the intercalated dodecanesulfonate from the monolayer to the bilayer structure or changing the tilt angle.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권3호
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• pp.247-252
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• 2021

Let M be a real hypersurface in a complex space form M_n(c), c ≠ 0. In this paper, we prove that if (∇_Xϕ)Y + (∇_Yϕ)X = 0 holds on M, then M is a Hopf hypersurface, where ϕ is the tangential projection of the complex structure of M_n(c). We characterize such Hopf hypersurfaces of M_n(c).

• East Asian mathematical journal
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• 제24권4호
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• pp.415-419
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• 2008

Let M be a generic submanifold of $S^n\;{\times}\;S^n$. If M admits an Sasakian structure, then M is a Brieskorn manifold.

• 대한수학회논문집
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• 제9권2호
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• Structural Monitoring and Maintenance
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• 제1권4호
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• pp.393-409
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• 2014

Across-wind response is often the cause of significant structural vibrations that in turn cause fatigue damage to welded and other connections. The efficacy of low-cost helical strakes to mitigate such adverse response is presented for a traffic signal structure. Field observations are made on a prototype structure in a natural wind environment without and with helical strakes installed on the cantilevered arm. Through continuous monitoring, the strakes were found to be effective in reducing across-wind response at wind speeds less than 10 m/s. Estimates of fatigue life are made for four different geographical locations and wind environments. Results for the class of traffic signal structure show that helical arm strakes are most effective in locations with benign wind environments where the average annual wind speed is not more than the vortex shedding wind speed, which for this investigation is 5 m/s. It is concluded that while strakes may be effective, it is not the panacea to mitigating connection fatigue at all locations.

• 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.