DIFFERENTIAL GEOMETRIC RESEARCH ON SUBMANIFOLDS AND STUDY OF SYSTEMS FOR THE EFFECTIVE DISSEMINATION OF RESEARCH

子流形的微分几何研究和研究有效传播的系统研究

基本信息

批准号：
09440038
负责人：
OGIUE Koichi
金额：
$ 7.62万
依托单位：
TOKYO METROPOLITAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

Differential Geometry is originated to the study of curves and surfaces in 3-dimensional Euclidian space and submanifold theory is a central research subject. One of this research project is to develop the differential geometric research of submanifolds and the study of its realted branches. Another is to construct and to work the systems for the effective dissemination of research in this field. In 1997, after the head investigator and investigators discussed working plans and made a setting of research aims and a choice of priority items in each division of project, and organized research groups led by each investigators, we started the research activities. First, in order to enable us effective exchange of informations, Nakamula and Hamada led to construct a mailing system and to start a use of the system. At present, 246 researchers of this area in the world belong to the system. In order to report research results in the environs of each investigators and to obtain informations fr … More om neighboring areas, we organized 4 conferences in 1997 and 4 conferences in 1998. They are extremely important on step up our research. Especially conferences inviting foreign researchers had much effect on enlarging our view. It was very advantageous that investigators joined international conferences outside the country and gave talks on their research results, and they were able to have information exchange with many foreign mathematicians. As results of these activities, Ogiue, Maeda, Adachi, Udagawa and others greatly contributed to give so many results in the study of curves (closed geodesics, circles, helixes) in specific Riemanninan manifolds and their submanifolds. Concerned with the study of surfaces and real hypersurfaces in spheres and complex projective spaces, Maeda, Takagi, Kitagawa and others provided many deep results. Strikingly, Miyaoka provided a wonderful progress in the classification problem since E. Cartan of isoparametric hypersurfaces in spheres, and Kenmotsu provided a big progress in the classification problem since E. Cartan of minimal surfaces with constant Gaussian curvature in complex projective spaces beginning from S.S. Chern's work. In the study of harmonic maps of Riemann surfaces into symmetric spaces and their realted minimal surfaces, Ejiri, Ohnita, Udagawa and others gaves several progress from the viewpoint of theory of integrable systems. From the viewpoint of singularity theory, knot theory, gauge theory, moduli spaces etc. and other neighboring branches, Izumiya, Ohara, Ohnita and others worked on this research project and gave new results. Based on these results of this project, we greatly expect the further progress of this area. Less

微分几何起源于三维欧氏空间中的曲线和曲面的研究，子流形理论是其核心研究课题之一，是开展子流形的微分几何研究及其相关分支的研究。 1997年，在首席研究员和研究人员讨论了工作计划并确定了各部门的研究目标和优先项目后，建立并运行了该领域研究的有效传播系统。项目，并组织了由每个研究者领导的研究小组，我们开始了研究活动，首先，为了使我们能够有效地交换信息，Nakamula和Hamada领导构建了一个邮件系统，并开始使用该系统。世界上有246名该领域的研究人员加入该系统，为了报告每个研究者所在地区的研究成果并获取邻近地区的信息，我们在1997年组织了4次会议，在2009年组织了4次会议。 1998年，他们对加强我们的研究非常重要，特别是邀请国外研究人员参加的会议对扩大我们的视野起到了很大的作用，研究人员参加国外的国际会议并发表他们的研究成果是非常有利的，他们能够进行研究。与许多外国数学家进行信息交流，荻上、前田、足立、宇田川等人在曲线（闭合测地线、圆、前田、高木、北川等人关注特定黎曼流形及其子流形中的曲面和真实超曲面的研究，提供了许多深刻的成果，自此以来，宫冈在分类问题上取得了进展。球体中等参超曲面的 E. Cartan，自 E. Cartan 具有常数的最小曲面以来，Kenmotsu 在分类问题上取得了重大进展复射影空间中的高斯曲率始于S.S. Chern的工作，在黎曼曲面到对称空间及其相关极小曲面的调和映射的研究中，Ejiri、Ohnita、Udakawa等人从可积系统理论的角度取得了一些进展。奇点理论、纽结理论、规范理论、模空间等以及其他邻近分支的观点，Izumiya、Ohara、Ohnita 等人对此进行了研究基于该项目的这些成果，我们非常期待该领域的进一步进展。