• 호남수학학술지
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• 제38권2호
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• pp.375-384
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• 2016

In this paper, we study the pseudo-symmetry of unit tangent sphere bundle. We prove that if the unit tangent sphere bundle $T_1M$ with standard contact metric structure over a locally symmetric $M^n$, $n{\geq}3$ is pseudo-symmetric, then M is of constant curvature.

• 전자공학회논문지S
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• 제35S권2호
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• pp.79-88
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• 1998

We developed a method for the solid angle estimation of acetabular coverage of the femoral head in 3D space. The superior half of the femoral head is modeled as part of a sphere. And the tangent lines connecting from a set of points of the acetabular outline to the center of the fitted sphere are obtained. The lines passthrough the unit sphere whose center is the same as that of the femoral head. The interesecting points form a boundary on the unit sphere. With the points on the unit sphere, we calculate the covered area of the femoral headand estimate the solid angle. Solid angle is defined asthe suface area within the boundary on the unit sphere. In this measurements, the solid angle of normal subjects is on an average 4.3(rad) and the corresponding acetabular coverage is 68%. Unlinke the conventional methods, this solid angle estimation shows real 3D acetabular coverage.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.79-86
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• 1998

In this paper, we study an (n ＋ 1)-dimensional compact, orientable, minimal contact CR-submanifold of (n - 1) ontact CR-dimension in a (2m ＋ 1)-dimensional unit sphere $S^{2m＋1}$ in terms of integral formula.

• 호남수학학술지
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• 제41권3호
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• pp.609-617
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• 2019

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.

• 호남수학학술지
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• 제42권4호
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• pp.811-819
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• 2020

We give characterizations of locally symmetric spaces M via the structural operator $h={\frac{1}{2}{\mathcal{L}}_{\xi}{\phi}}$ or the characteristic Jacobi operator ℓ = R(·, ξ)ξ on the unit tangent sphere bundles T1M.

• 대한수학회논문집
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• 제13권3호
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• pp.561-577
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• 1998

We study (n＋3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of $S^{4r＋3}$(a) $\times$ $S^{4s＋3}$(b) ($a^2$＋ $b^2$=1, 4(r ＋ s) = n - 3) as a contact three CR sub manifold of a (4m＋3)-dimensional unit sphere.

• 대한수학회보
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• 제47권3호
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• 대한수학회보
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• 제44권1호
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• pp.109-116
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• 2007

We study an (n+1)($(n{\geq}3)$-dimensional contact CR-submanifold of (n-1) contact CR-dimension in a (2m+1)-unit sphere $S^{2m+1}$, and to determine such sub manifolds under conditions concerning the second fundamental form and the induced almost contact structure.

• 대한수학회지
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• 제48권2호
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• pp.329-340
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• 2011

We shall give some curvature conditions for the unit tangent sphere bundle of an n($\geq$ 4)-dimensional Riemannian manifold to be H-contact. Furthermore, we provide an example illustrating Main Theorem.

• 대한수학회보
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• 제50권5호
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• pp.1599-1622
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• 2013

We show many examples of curves on the unit 2-sphere $S^2(1)$ in $\mathbb{R}^3$ and the unit 3-sphere $S^3(1)$ in $\mathbb{R}^4$. We study whether its curves are Bertrand curves or spherical Bertrand curves and provide some examples illustrating the resultant curves.