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 RUAN这个项目在于Kahler几何形状及其用于镜面对称性的区域。更具体地说，研究者是使用卡勒或里曼尼亚崩溃的概念 - 一系列卡勒歧管及其极限歧管的序列被考虑 - 进一步进一步了解我们对镜像对称性的理解。 Riemannian歧管是配备有距离概念的弯曲空间，也称为度量。 （紧凑的）Riemannian歧管本身的总体可以给出一个度量，以便在无限收集此类歧管时，谈论聚类或收敛是有意义的。镜面对称性是物理学家最初发现的现象：在流行的10维弦理论模型中，即无形的6维出现了，如具有某些对称性的Calabi-yau歧管所谓的calabi-yau歧管。