• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.935-949
• /
• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

• Journal of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.147-157
• /
• 2006

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an antide Sitter space $H_1^4(-1)$. It is proved that complete maximal spacelike hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $H_1^4(-1)$ are isometric to the hyperbolic cylinder $H^2(c1){\times}H^1(c2)$ with S = 3 or they satisfy $S{\leq}2$, where S denotes the squared norm of the second fundamental form.

• The Pure and Applied Mathematics
• /
• v.20 no.3
• /
• pp.149-158
• /
• 2013

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.12
• /
• pp.3007-3019
• /
• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

• Honam Mathematical Journal
• /
• v.38 no.4
• /
• pp.739-752
• /
• 2016

The main aim of this paper is to introduce an extension of the generalized ${\tau}$-Gauss hypergeometric function $_rF^{\tau}_s(z)$ and investigate various properties of the new function such as integral representations, derivative formulas, Laplace transform, Mellin trans-form and fractional calculus operators. Some of the interesting special cases of our main results have been discussed.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.509-518
• /
• 1995

Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

• Communications of the Korean Mathematical Society
• /
• v.13 no.3
• /
• pp.589-594
• /
• 1998

쌍곡공간$^3$에 들어있는 닫힌 곡면의 주곡률함수가 특별한 함수 관계를 만족시킨다면 그 곡면은 둥근공임을 보였다. 이 결과를 이용하여 Gauss-Kronecker 곡률이 상수인 닫힌 곡면은 둥근공 뿐이 없음도 보였다.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.305-315
• /
• 1997

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.429-437
• /
• 1994

Let $M^n$ be a connected hypersurface in Euclidean (n + 1)-space $E^{n+1}$, and let $G : G^n \longrightarrow S^n(1) \subset E^{n+1}$ be its Gauss map.

• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.325-330
• /
• 2000

3차원 Euclid 공간의 볼록폐곡면의 평균곡률과 Gauss 곡률의 비가 상수함수와 충분히 가까우면 그 곡면은 중심이 같고 반지름이 거의 같은 두 개의 둥근공 사이에 놓이게 됨을 보였다.