• 대한수학회논문집
• /
• 제18권2호
• /
• pp.309-323
• /
• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• 제어로봇시스템학회논문지
• /
• 제10권5호
• /
• pp.415-420
• /
• 2004

We present a new algorithm for the calibration of a camera and the recovery of 3D scene structure up to a scale from image sequences using known angles between lines in the scene. Traditional method for calibration using scene constraints requires various scene constraints due to the stratified approach. Proposed method requires only one type of scene constraint of known angle and also it directly recovers metric structure up to an unknown scale from projective structure. Specifically, we recover the matrix that is the homography between the projective structure and the Euclidean structure using angles. Since this matrix is a unique one in the given set of image sequences, we can easily deal with the problem of varying intrinsic parameters of the camera. Experimental results on the synthetic and real images demonstrate the feasibility of the proposed algorithm.

• 대한수학회지
• /
• 제33권3호
• /
• pp.625-639
• /
• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1315-1327
• /
• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• 호남수학학술지
• /
• 제30권3호
• /
• pp.535-550
• /
• 2008

Let M be a real hypersurface of a complex space form with almost contact metric structure $({\phi},{\xi},{\eta},g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

• 호남수학학술지
• /
• 제31권2호
• /
• pp.185-201
• /
• 2009

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant.

• 대한수학회보
• /
• 제34권4호
• /
• pp.549-560
• /
• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• 대한수학회지
• /
• 제32권3호
• /
• pp.471-482
• /
• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• 대한수학회지
• /
• 제43권6호
• /
• pp.1231-1252
• /
• 2006

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space ${\Im}(M)$ into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on ${\Im}(M)$.

• 정보처리학회논문지B
• /
• 제17B권3호
• /
• pp.183-188
• /
• 2010

본 연구에서는 여러 이미지를 이용하여 사실적인 3차원 장면의 모델을 얻는 방법이 구현되었다. 이미지는 파라메터를 모르는 카메라를 이용하여 여러 위치에서 획득한 것을 사용하였다. 먼저 특징점 추출 및 추적 방법을 사용하여 모든 이미지에 대한 대응점들을 구하고 이 점들을 사용하여 사영복원을 구한다. 그 다음 사영 복원된 값에 여러 제약조건을 사용하여 유클리디언 복원을 하면 특징점들의 3차원 좌표값이 계산된다. 이 좌표값을 이용하여 삼각형 메쉬를 구한 후 이 면에 텍스처 맵핑을 하면 사실적인 복원이 완성된다. 전체 시스템은 C++언어로 구현하였으며, 사용자 인터페이스는 Qt 라이브러리로, 텍스처 맵핑과 모델 가시화 부분은 OpenGL 그래픽스 라이브러리로 구현하였다. 구현된 시스템의 효용성을 보이기 위해 모의 데이터와 실제 이미지 데이터를 이용하여 실험한 결과를 포함하였으며 만족할 만한 복원 결과를 얻을 수 있었다.