Mathematical Sciences: Real Submanifolds and Holomorphic Functions

数学科学：实子流形和全纯函数

• 批准号: 9201966
• 负责人: Sidney Webster
• 金额: $ 10.02万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201966&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Real; Submanifolds; Holomorphic

The principal investigator will focus on two lines of research in the theory of functions of several complex variables. He will study the holomorphic symplectic geometry of real functions and the holomorphic contact geometry of real submanifolds. He will also study the regularity of a particular solution to the integrability problem for CR structures and for CR vector bundles. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.

首席研究员将重点关注多个复变量函数理论的两条研究方向。 他将研究实函数的全纯辛几何和实子流形的全纯接触几何。他还将研究 CR 结构和 CR 向量丛的可积问题的特定解决方案的规律性。 该奖项将支持微分几何和全局分析一般领域的研究。微分几何是研究空间几何形状与空间上定义的解析概念之间关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。