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 Grahamthis项目将研究保形和CR几何形状。 代数，分析和几何方面将通过引入与原始整形型或Crgeometry相关的指标引入更高的尺寸来考虑。 了解较高的维空间会引起独立利益的问题。 动机是由物理学中的ADS/CFTCORTENCE提供的。符合形式的几何形状是对空间的性质的研究，而空间的属性是不变的，这些转换可以保留角度但不一定是长度的。概要映射和几何形状已经在多年来对实用问题进行了许多应用，例如飞机机翼的设计。 最近，在较高维度中的保形测定法已成为物理学中所谓的全息相对次数引起了很多兴趣的对象。 该项目将研究基础几何空间的特性，部分是由与物理理论相互作用的部分动机。