Mathematical Sciences: Riemannian Geometry of Lagrangian Submanifolds

数学科学：拉格朗日子流形的黎曼几何

• 批准号: 9012367
• 负责人: Yong-Geun Oh
• 金额: $ 1.18万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-01 至 1991-12-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012367&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Riemannian; Geometry; Lagrangian

The principal investigator will study various aspects of Lagrangian submanifolds in symplectic geometry. This will involve an analysis of the relationship between symplectic structures and the Riemannian structure of Kahler manifolds. This investigation will include, as a model case, the study of minimal submanifolds and their mean curvature evolutions. Symplectic geometry has a long history of success as a framework in which difficult questions in mechanics can be formulated and solved. The principal investigator will use connections between this theory and complex Kahler manifolds especially as related to minimal submanifolds. Such surfaces are modeled by soap films and have been the objects of intense mathematical research in recent years.

主要研究人员将研究辛几何中拉格朗日子流形的各个方面。这将涉及到Kahler流形的辛结构和黎曼结构之间的关系的分析。作为一个典型案例，这项研究将包括极小子流形及其平均曲率演化的研究。辛几何作为一个框架已经有了很长的成功历史，在这个框架中可以表述和解决力学中的困难问题。主要研究人员将利用这一理论与复Kahler流形之间的联系，特别是与极小子流形有关的联系。这种表面是由肥皂膜模拟的，近年来一直是密集的数学研究的对象。