Mathematical Sciences: Symplectic Topology & Riemannian Geometry of Lagrangian Submanifolds

数学科学：辛拓扑

• 批准号: 9504455
• 负责人: Yong-Geun Oh
• 金额: $ 7.5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504455&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Topology; &amp

9504455 Oh The proposed research lies in the general area of symplectic topology and geometry. More specifically, the investigator proposes to study Floer cohomology and Lagrangian submanifolds. It is expected that such a study will lead to new techniques for Lagrangian embedding and immersion problems. In addition, the investigator proposes to consider curvature estimate problems for special Lagrangian submanifolds - this may have ramifications in minimal submanifold theory. Symplectic geometry provides a rigorous mathematical setting for many problems in classical and quantum mechanics. Lagrangian submanifolds are fundamental objects - they are extremal objects in some sense - in symplectic geometry, Floer cohomology is a powerful topological tool for their study.

9504455哦，拟议的研究在于符号拓扑和几何形状的一般领域。更具体地说，研究人员提议研究浮子同居和拉格朗日亚曼佛群岛。预计这样的研究将导致拉格朗日嵌入和沉浸问题的新技术。此外，研究者建议考虑特殊拉格朗日亚曼福尔德的曲率估计问题 - 这可能在最小的亚曼菲德理论中产生了影响。 符号几何形状为经典和量子力学中的许多问题提供了严格的数学设置。拉格朗日亚曼菲尔德是基本对象 - 从某种意义上说，它们是极端对象 - 在符号几何形状中，浮动的共同体学是其研究的强大拓扑工具。