Mathematical Sciences: Harmonic Maps, Foliations, and Manifolds with Special Holomony

数学科学：调和图、叶状结构和具有特殊全调的流形

• 批准号: 9203765
• 负责人: Kevin Corlette
• 金额: $ 2万
• 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: 1992-08-15 至 1993-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203765&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Maps; Foliations

The principal investigator will continue his research on harmonic maps, foliations, and manifolds with special holonomy groups. In particular, he will study rigidity for lattices in certain rank one Lie groups, quotients of rank one symmetric spaces, and flat vector bundles over Kahler manifolds. 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.

首席研究员将继续他对具有特殊完整群的调和映射、叶层和流形的研究。特别是，他将研究某些一阶李群、一阶对称空间的商以及Kahler流形上的平坦向量丛的格的刚性。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。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性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。