Mathematical Sciences: On Certain Rigidity Problems in Kaehler Geometry

数学科学：关于凯勒几何中的某些刚性问题

• 批准号: 9105185
• 负责人: Fangyang Zheng
• 金额: $ 3.6万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105185&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Certain; Rigidity; Problems

The uniformization theorem of one complex variable completely classifies the one dimensional simply connected complex manifolds. There is no corresponding result for higher dimensional complex manifolds and it is important to try to find some method which will provide a substitute classification. The principal investigator will try to classify those higher dimensional complex manifolds which satisfy a pinched curvature condition. Classification of a set of objects which satisfy a common property or condition is one tool mathematicians use to understand structures and their relationships. If one can list all objects which have a restricted common property, then one better understands the property and the objects. The principal investigator will attempt to do this with manifolds or surfaces whose curvature falls between certain bounds.

一个复变量的一致化定理完全地分类了一维单连通复流形。对于高维复杂流形没有相应的结果，重要的是试图找到一种方法来提供一种替代分类。主要研究人员将尝试对满足收缩曲率条件的高维复杂流形进行分类。对满足共同性质或条件的一组对象进行分类是数学家用来理解结构及其关系的工具。如果可以列出具有受限公共属性的所有对象，则可以更好地理解属性和对象。主要的研究人员将尝试对曲率落在特定界限之间的流形或曲面进行这项研究。