Convergence and Collapsing of Kahler Manifolds and Mathematical Theory of Mirror Symmetry

卡勒流形的收敛与塌缩与镜像对称的数学理论

• 批准号: 9703870
• 负责人: Wei-Dong Ruan
• 金额: $ 7.85万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703870&HistoricalAwards=false
• 关键词: Convergence; Collapsing; Kahler; Manifolds; Mathematical

9703870 Ruan This project lies in the area of Kahler geometry and its application to mirror symmetry. More specifically, the investigator is to use the idea of Kahler or Riemannian collapsing - a sequence of Kahler manifolds and their limit manifold are considered - to further our understanding of mirror symmetry. Riemannian manifolds are curved spaces equipped with a notion of distance, also called a metric. The totality of (compact) Riemannian manifolds itself can be given a metric so that when given an infinite collection of such manifolds it makes sense to talk about clustering or converging. Mirror symmetry is a phenomenon first discovered by physicists: in the popular 10-dimensional string theory model of the universe, the invisible 6-dimensions arise as so called Calabi-Yau manifolds possessing certain symmetry.

9703870阮这个项目属于Kahler几何及其在镜像对称中的应用。更具体地说，研究者将使用Kahler或riemanian坍缩的概念——考虑Kahler流形序列及其极限流形——来进一步理解镜像对称。黎曼流形是具有距离概念的弯曲空间，也称为度规。（紧）黎曼流形的总体本身可以给定一个度规，因此当给定这样的流形的无限集合时，讨论聚类或收敛是有意义的。镜像对称是物理学家首先发现的一种现象：在流行的10维宇宙弦理论模型中，不可见的6维以具有一定对称性的所谓Calabi-Yau流形出现。