Problems Related to Conformal and CR Geometry

与共形和 CR 几何相关的问题

• 批准号: 0204480
• 负责人: C. Robin Graham
• 金额: $ 13.17万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204480&HistoricalAwards=false
• 关键词: Problems; Related; Conformal; CR; Geometry

ABSTRACT DMS - 0204480. PI: C. Robin GrahamThis project will study conformal and CR geometry. Algebraic, analytic,and geometric aspects will be considered via the introduction of metrics inhigher dimensions which are associated to the original conformal or CRgeometry. Understanding the higher dimensional spaces gives rise to problemsof independent interest. Motivation is provided by the AdS/CFTcorrespondence in physics.Conformal geometry is the study of properties of space which are unchangedby transformations which preserve angles but not necessarily lengths.Conformal mapping and geometry has found numerous applications to practicalproblems for many years, such as the design of airplane wings. Conformalgeometry in higher dimensions has recently been the object of much interestin so-called holographic correspondences in physics. This project willstudy properties of the underlying geometric spaces, partially motivated bythe interaction with the physical theories.

摘要 DMS - 0204480。 PI：C. Robin Graham 该项目将研究共形和 CR 几何。 将通过引入与原始共形或 CR 几何相关的更高维度的度量来考虑代数、分析和几何方面。 理解更高维度的空间会引起独立兴趣的问题。 物理学中的 AdS/CFT 对应提供了动机。共形几何是对空间属性的研究，空间属性不会因保留角度但不一定保留长度的变换而改变。多年来，共形映射和几何在实际问题中得到了广泛的应用，例如飞机机翼的设计。 高维度的共形几何最近成为物理学中所谓的全息对应的人们非常感兴趣的对象。 该项目将研究底层几何空间的属性，部分是由与物理理论的相互作用推动的。