• 대한수학회보
• /
• 제49권2호
• /
• pp.285-293
• /
• 2012

In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.

• Kyungpook Mathematical Journal
• /
• 제50권4호
• /
• pp.509-536
• /
• 2010

In this paper, we investigate curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples and is included by that of curvature-adapted and isoparametric submanifolds with flat section. First we introduce the notion of a focal point of non-Euclidean type on the ideal boundary for a submanifold in a Hadamard manifold and give the equivalent condition for a curvature-adapted and complex equifocal submanifold to be proper complex equifocal in terms of this notion. Next we show that the complex Coxeter group associated with a curvature-adapted and proper complex equifocal submanifold is the same type group as one associated with a principal orbit of a Hermann type action and evaluate from above the number of distinct principal curvatures of the submanifold.

• 대한수학회논문집
• /
• 제17권2호
• /
• pp.261-278
• /
• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• 대한수학회논문집
• /
• 제13권4호
• /
• pp.825-838
• /
• 1998

We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽$_{ξ/}$S = 0 and Sξ = $\sigma$ξ for a smooth function $\sigma$, then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.

• 한국HCI학회:학술대회논문집
• /
• 한국HCI학회 2006년도 학술대회 1부
• /
• pp.871-877
• /
• 2006

물체의 반사(specular reflection)는 물체의 재질 및 기하학적 모양을 표현하는데 있어 매우중요한 요소이다. 사진품질의 사실적 렌더링에서는 기존의 국소 반사 모델을 사용하여 좋은 결과를 얻을 수 있지만, 사용자의 주관이 중시되는 비사실적 렌더링(non-photorealistic rendering)에서는 사용자가 원하는 반사 효과를 표현할 수 있어야 한다. 텍스처는 사용자가 직관적으로 원하는 반사 효과를 표현할 수 있는 수단이며, 이를 모델에 투영하면 원하는 반사효과를 얻을 수 있다. 이 때 사용자는 텍스처가 투영될 위치와 크기, 방향을 직접 키프레임으로 정해 줄 수 있다. 그러나 모든 반사 효과를 사용자가 직접 정해준다는 것은 번거로운 일이며, 실시간 응용분야에는 적용할 수 없다. 본 논문에서는 국소반사모델(local reflection model)과 주곡률(principal curvature) 해석을 통해 반사효과의 위치, 방향, 크기를 결정하기 위한 텍스처 투영기의 새로운 설정 방법을 제시한다. 광원과 시점 정보를 사용하여 투영기의 위치를 정하고 물체의 주방향(principal direction)과 곡률반지름(radius of curvature)을 이용하여 투영기의 방향과 투영 피라미드의 크기를 정한다 텍스처 투영기의 단순한 이동, 회전을 통하여 반사 영역의 이동, 회전 및 확대/축소가 가능하다. 본 논문에서 제시한 방법은 DirectX 9.0c와 프로그래이 가능한 셰이더 2.0을 사용하여 GeForce FX 7800 그래픽 카드에 구현되었다. 본 논문의 연구 결과는 게임과 같은 실시간 응용분야에 사용될 수 있으며, 실험 결과에 의하면 수천 개의 다면체 모델에 대한 렌더링을 실시간에 수행할 수 있다.

• 대한수학회보
• /
• 제49권4호
• /
• pp.685-692
• /
• 2012

Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.

• 대한수학회보
• /
• 제36권4호
• /
• pp.701-706
• /
• 1999

A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature $H_1$ does not vanish and the ratio $H_n$/$H_1$ of the Gauss-Kronecker curvature $H_n$ and $H_1$ is constant.

• Geomechanics and Engineering
• /
• 제18권2호
• /
• pp.141-151
• /
• 2019

In this paper, it is aimed to present a detail investigation about the comparison of static and dynamic behavior of historical masonry arch bridges considering different arch curvature. $G{\ddot{o}}derni$ historical masonry two-span arch bridge which is located in Kulp town, Diyarbakir, Turkey is selected as a numerical application. The bridge takes part in bowless bridge group and built in large measures than the others. The restoration projects were approved and rehabilitation studies have still continued. Finite element model of the bridge is constituted with special software to determine the static and dynamic behavior. To demonstrate the arch curvature effect, the finite element model are reconstructed considering different arch curvature between 2.86 m-3.76 m for first arch and 2.64 m-3.54 m for second arch with the increment of 0.10 m, respectively. Dead and live vehicle loads are taken into account during static analyses. 1999 Kocaeli earthquake ground motion record is considered for time history analyses. The maximum displacements, principal stresses and elastic strains are compared with each other using contour diagrams. It is seen that the arch curvature has more influence on the structural response of historical masonry arch bridges. At the end of the study, it is seen that with the increasing of the arch heights, the maximum displacements, minimum principal stresses and minimum elastic strains have a decreasing trend in all analyses, in addition maximum principal stresses and maximum elastic strains have unchanging trend up to optimum geometry.

• 대한수학회지
• /
• 제55권3호
• /
• pp.553-574
• /
• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• 호남수학학술지
• /
• 제28권1호
• /
• pp.141-164
• /
• 2006

Let $G=O(2){\times}O(2){\times}O(2)$ and let $M^4$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$. In this paper, we prove a property on $M^4$.