Mathematical Sciences: Differential Geometry

数学科学：微分几何

• 批准号: 9001089
• 负责人: Wu-Yi Hsiang
• 金额: $ 46.7万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001089&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry

Five investigators will study problems in contemporary differential geometry which have close relations to nonlinear and linear partial differential equations. Among the areas of special emphasis are the geometry of submanifolds, symplectic and Poisson geometry, Gauge theory in principal bundles, Lie transformation groups, and complex manifolds. Differential geometry is an outgrowth of multi-variable calculus. Physics has been a rich source of unsolved problems which may be phrased naturally in differential geometric terms. Among these are questions arising from the geometry of space and time first understood by Einstein. Gauge theory is an attempt to go beyond these earlier studies toward a theory which explains both the physics of the small and of the large. This group of differential geometers will study a variety of problems related to modern gauge theory.

五名研究人员将研究当代 微分几何与非线性、 线性偏微分方程 的区域中底 特别强调的是几何的子流形，辛和 泊松几何，主丛规范理论，李 变换群和复流形。 微分几何是多元几何的产物 微积分 物理学一直是未解决问题的丰富来源 其可以用微分几何术语自然地表达。 这些问题中有空间几何学引起的问题， 爱因斯坦最早理解的时间 规范理论试图 超越了这些早期的研究， 无论是小的物理学还是大的物理学 这群 微分几何学家将研究各种各样的问题， 现代规范理论