Mathematical Sciences: Intrinsic and Extrinsic Curvature of Singular Spaces

数学科学：奇异空间的本征曲率和外征曲率

• 批准号: 9101871
• 负责人: Joseph H. Fu
• 金额: $ 3.62万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101871&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Intrinsic; Extrinsic; Curvature

Professor Fu will study possible analogs of scalar-valued curvatures on singular spaces. The principal investigator has already made some progress in this direction and will try to extend his work from special cases to more general singular spaces. The primary method to be used in the investigation is geometric measure theory. One of the goals of this research is to understand how classical invariants of geometry such as curvature can be extended to singular spaces, that is, spaces with corners, cusps, or self intersections. These classical invariants are very important in our understanding of the geometry of a space and the extension of these concepts to singular spaces, which are playing an increasingly central role in the modeling of physical systems, should have immediate application.

傅教授将研究标量值的可能类似物 奇异空间上的曲率主要研究者 已经在这方面取得了一些进展，并将努力扩大 他的工作从特殊情况下更一般的奇异空间。的 在调查中使用的主要方法是几何测量 理论 这项研究的目标之一是了解 几何学的经典不变量，如曲率， 到奇异空间，即有角、尖点或自我的空间 路口这些经典不变量在我们的 理解空间的几何形状以及这些几何形状的延伸 奇异空间的概念，这是发挥越来越多的 物理系统建模的核心作用，应该有 立即应用。