• East Asian mathematical journal
• /
• 제10권2호
• /
• pp.397-403
• /
• 1994

• 호남수학학술지
• /
• 제23권1호
• /
• pp.113-132
• /
• 2001

We prove an equality that holds on G-invariant minimal hypersurfaces with constant scalar curvatures in $S^5$.

• Kyungpook Mathematical Journal
• /
• 제56권4호
• /
• pp.1207-1235
• /
• 2016

Let M be a real hypersurface with constant mean curvature in a complex space form $M_n(c),c{\neq}0$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}= R({\cdot},{\xi}){\xi}$ with respect to the structure vector field ${\xi}$ is ${\phi}{\nabla}_{\xi}{\xi}$-parallel and $R_{\xi}$ commute with the structure tensor field ${\phi}$, then M is a homogeneous real hypersurface of Type A.

• 대한수학회논문집
• /
• 제24권2호
• /
• pp.265-275
• /
• 2009

The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.

• 한국군사과학기술학회지
• /
• 제13권4호
• /
• pp.642-649
• /
• 2010

LOS analysis is used for optimal deployment of mid-range guided weapon system or system engagement effectiveness simulation. Comparing to real-world, LOS analysis includes error sources such as coarse terrain data resolution, refraction of radio waves, and several ideal assumptions. In this research, exact LOS algorithm under assumption of constant earth curvature and error analysis of that is investigated. It proved that LOS algorithm under assumption of constant earth curvature has negligible error in mid-range guidance weapon system's scope.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1539-1550
• /
• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• 충청수학회지
• /
• 제26권3호
• /
• pp.601-603
• /
• 2013

We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone $C{\subset}\mathbb{R}^{n+1}$ is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ${\partial}C$.

• 대한수학회보
• /
• 제41권1호
• /
• pp.117-123
• /
• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• 대한수학회보
• /
• 제50권1호
• /
• pp.135-142
• /
• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• 대한수학회보
• /
• 제37권3호
• /
• pp.641-648
• /
• 2000

It has been conjectured that, on a compact 3-dimensional manifold, a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics of volume 1 is Einstein. In this paper we find a sufficient condition that a critical point is Einstein. This condition is equivalent for a critical point ot be conformally flat. Its relationship with the Fisher-Marsden conjecture is also discussed.