Mathematical Sciences: The Structure of Cycle Spaces, Algebraic Manifolds, and Einstein Spaces

数学科学：循环空间、代数流形和爱因斯坦空间的结构

• 批准号: 8901303
• 负责人: H. Blaine Lawson
• 金额: $ 43.96万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901303&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Cycle; Spaces

A team of four geometers will investigate a variety of problems in complex differential geometry, Riemannian geometry, and related areas. The role of spaces of algebraic cycles in universal constructions in topology and homology-cohomology theory will be carefully studied. Work will progress on establishing the existence of Kahler-Einstein metrics on open manifolds, on the structure of p-Kahler spaces in Moishezon geometry, and on the structure of Riemannian 4-manifolds with boundary. The team of investigators will establish more of the ground work necessary for the understanding by physicists of our four dimensional space-time. The connections between the branch of mathematics broadly referred to as "differential geometry," and cosmological physics dates back to Einstein; the mathematical theory which Einstein applied goes back even further to Gauss and Riemann in the nineteenth century. The group being funded here maintains close connections with physicists, and steers their research in directions of current excitement both to mathematicians and physicists.

由四位几何学家组成的团队将研究复杂微分几何、黎曼几何和相关领域的各种问题。 将仔细研究代数环空间在拓扑和同调上同调理论中的普遍构造中的作用。 工作将在确定开流形上卡勒-爱因斯坦度量的存在性、Moishezon 几何中的 p-卡勒空间结构以及带边界的黎曼 4 流形结构方面取得进展。 研究小组将为物理学家理解我们的四维时空建立更多必要的基础工作。 广义上称为“微分几何”的数学分支与宇宙物理学之间的联系可以追溯到爱因斯坦。爱因斯坦所应用的数学理论可以追溯到十九世纪的高斯和黎曼。这里资助的小组与物理学家保持着密切的联系，并将他们的研究引导到当前令数学家和物理学家兴奋的方向。