• 대한수학회지
• /
• 제40권4호
• /
• pp.695-708
• /
• 2003

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

• 대한수학회지
• /
• 제37권2호
• /
• pp.193-223
• /
• 2000

In the late 1970's, M. Kuranishi proposed to control the moduli of the germ of a normal Stein space by deformations of the CR structure on the boundary. I this paper, we will see that it is naturally accomplished by considering stably embeddable deformations of CR structures.

• 대한수학회지
• /
• 제40권4호
• /
• pp.667-680
• /
• 2003

The mirror conjecture means originally the deep relation between complex and symplectic geometry in Calabi-Yau manifolds. Recently, this conjecture is posed beyond Calabi-Yau, and even to, open manifolds (e.g. $A_{n}$ singularities and its resolution) is discussed. While if we treat open manifolds, we can't avoid the boundary (in our case, CR manifolds). Therefore we pose the more precise conjecture (mirror symmetry with boundaries). Namely, in mirror symmetry, for boundaries, what kind of structure should correspond\ulcorner For this problem, the $A_{n}$ case is studied.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제11권3호
• /
• pp.175-187
• /
• 2004

The purpose of the present paper is to study the generalized CR-sub manifold of a T-manifold. After preliminaries we have studied the integrability of the distributions and obtained the conditions for integrability. Then geometry of leaves are being studied. Finally it is proved that every totally umbilical generalized CR-submanifold of a T-manifold is totally geodesic.

• Kyungpook Mathematical Journal
• /
• 제56권3호
• /
• pp.965-977
• /
• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.

• East Asian mathematical journal
• /
• 제25권4호
• /
• pp.495-504
• /
• 2009

We introduce three classes of quaternion lightlike submanifolds, screen real lightlike submanifolds and CR lightlike submanifolds of an indefinite quaternion Kaehlerian manifold and study the geometry of leaves of their distributions.

• 한국멀티미디어학회논문지
• /
• 제9권8호
• /
• pp.982-999
• /
• 2006

본 논문에서는 복합 칼라정보와 얼굴의 기하학적 정보를 이용한 인터넷 기반 얼굴관상해석 및 자동 얼굴 컨텐츠 생성시스템을 제안하였다. 제안한 시스템은 YCbCr과 YIQ 칼라모델의 Cr과 I 성분의 논리곱 연산처리로 얼굴영역을 검출하였다. 검출한 얼굴영역에서 얼굴의 기하학적 정보로부터 얼굴 특징자를 추출 하였으며 각 특징자들을 세부 분류하여 얼굴 관상을 해석하도록 하였다. 또한 제안한 시스템은 추출과 분류된 특징자로부터 개인의 얼굴에 가장 적합한 얼굴 아바타 컨텐츠를 자동 생성할 수 있게 하였다. 실험결과 제안한 방법은 기존의 얼굴인식 방법에 비해 실시간 얼굴검출과 인식은 물론 정량적인 얼굴관상해석과 자동 얼굴 아바타 생성이 가능하였다.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2002년도 하계종합학술대회 논문집(4)
• /
• pp.57-60
• /
• 2002

Facial features are often used for human computer interface(HCI). This paper proposes a method to detect facial features using color and facial geometry information. Face region is first extracted by using color information, and then the pupils are detected by applying a separability filter and facial geometry constraints. Mouth is also extracted from Cr(coded red) component. Experimental results shows that the proposed detection method is robust to a wide range of facial variation in position, scale, color and gaze.

• 호남수학학술지
• /
• 제46권1호
• /
• pp.47-59
• /
• 2024

The purpose of the Nash embedding theorem was to take extrinsic help for studying the intrinsic Riemannian geometry. To realize this aim in actual practice there is a need for optimal relationships between the known intrinsic invariants and the main extrinsic invariants for Riemannian submanifolds. This paper aims to provide an optimal relationship for CR-warped product submanifolds of locally conformal Kähler manifolds.

• 대한수학회지
• /
• 제43권5호
• /
• pp.1019-1045
• /
• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.