Mathematical Sciences: Harmonic Maps, Kahler Manifolds and Hermitian Locally Symmetric Spaces

数学科学：调和映射、卡勒流形和厄米局部对称空间

• 批准号: 9204095
• 负责人: Masatake Kuranishi
• 金额: $ 15.97万
• 依托单位: Columbia University
• 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 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204095&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Harmonic; Maps; Kahler

The principal investigator will study harmonic maps on a compact Riemannian manifold which is either Kahler or Riemannian locally symmetric. He will attempt to obtain new Bochner identities to prove geometric rigidity theorems in optimal for quotients of Riemannian symmetric manifolds of rank greater than one. His methods are different than standard methods in the line of research since he does not require that the manifolds under consideration be folliated by bounded symmetric domains. 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.

主要研究者将研究紧致黎曼流形上的调和映射，紧致黎曼流形是Kahler或黎曼局部对称的。他将尝试获得新的Bochner恒等式，以证明关于秩数大于1的黎曼对称流形的商的最优几何刚性定理。他的方法与研究领域的标准方法不同，因为他不要求所考虑的流形是由有界对称域划分的。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。