• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• 대한수학회보
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• 제53권4호
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• pp.1259-1280
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• 2016

The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

• 대한수학회지
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• 제56권4호
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• pp.917-934
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• 2019

In this paper, we give some classifications of almost Kenmotsu 3-manifolds under homogeneity and some symmetry conditions.

• The Journal of the Acoustical Society of Korea
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• 제17권1E호
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• pp.70-75
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• 1998

The analysis of dynamic responses are carried out on several anisotropic systems due to buried pulsating line sources. These include infinite, semi-infinite spaces. The media possess orthotropic or higher symmetry. The load is in the from of a normal stress acting with parallel to symmetry axis on the plane of symmetry within the materials. The results are first derived for infinite media. Subsequently the results for semi-infinite are derived by using superposition of the solution in the infinite medium together with a scattered solution from the boundaries. The sum of both solutions has to satisfy stress free boundary conditions, thereby leading to the complete solutions. The solutions are simplified to the systems possessing of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic symmetry.

• 대한수학회논문집
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• 제38권4호
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• pp.1271-1280
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• 2023

The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)_n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)_n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

• 소음진동
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• 제8권5호
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• pp.974-980
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• 1998

본 논문은 직교이방성 탄성계에서 내부 선형하중에 의한 탄성파의 거동을 고찰하였다. 첫째로, 내부 발진원에 대한 탄성과 거동식을 무한계와 반구계에서의 직교이방성 매체에서 유도하였고, 둘째로 Cargniard-DeHoop을 이용하여 순간선형하중에 대한 무한계와 반구계에서의 탄성과 거동식을 유도하였다. 반구계에서 탄성파에 대한 거동식은 무한계에서 유도한 결과와 반구의 표면에서 분산되는 반사파의 합으로 표현되고, 경계영역에서 경계조건을 만족하였다. 여러 가지 이방성 매체에 대한 수치해석 결과를 제시하였고, 이방성 매체의 특성인 bulk wave의 Lacunae 및 표면파의 영향을 고찰할 수 있었다. 본 논문의 결과는 지진연구, 복합소재 특성 연구, 지능형소재 특성연구 등에 응용될 것이다.

• 대한수학회보
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• 제51권1호
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.

• 대한수학회논문집
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• 제36권1호
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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.

• The Journal of the Acoustical Society of Korea
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• 제17권2E호
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• pp.53-58
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• 1998

In this paper, we study the response of several anisotropic systems to buried transient line loads. The problem is mathematically formulated based on the equations of motion in the constitutive relations. The load is in form of a normal stress acting with arbitrary axis on the plane of monoclinic symmetry. Plane wave equation is coupled with vertical shear wave, longitudinal wave and horizontal shear wave. We first considered the equation of motion in reference coordinate system, where the line load is coincident with symmetry axis of the orthotrioic material. Then the equation of motion is transformed with respect to general coordiante system with azimuthal angle by using transformation tensor. The load is first described as a body force in the equations of the motion for the infinite media and then it is mathematically characterized. Subsequently the results for semi-infinite spaces is also obtained by using superposition of the infinite medium solution together with a scattered solution from the free surface. Consequently explicit solutions for the displacements are obtained by using Cargniard-DeHoop contour. Numerical results which are drawn from concrete examples of orthotropic material belonging to monoclinic symmetry are demonstrated.

• 대한수학회보
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• 제57권1호
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• pp.139-165
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• 2020

Mirror symmetry for del Pezzo surfaces was studied in [3] where they suggested that the mirror should take the form of a Landau-Ginzburg model with a particular type of elliptic fibration. This argument came from symplectic considerations of the derived categories involved. This problem was then considered again but from an algebro-geometric perspective by Gross, Hacking and Keel in [8]. Their construction allows one to construct a formal mirror family to a pair (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. In the case where the self intersection matrix for D is not negative semi-definite it was shown in [8] that this family may be lifted to an algebraic family over an affine base. In this paper we perform this construction for all smooth del Pezzo surfaces of degree at least two and obtain explicit equations for the mirror families and present the mirror to dP₂ as a double cover of ℙ².