Mathematical Sciences: Differential Structures

数学科学：微分结构

• 批准号: 9001956
• 负责人: Eugenio Calabi
• 金额: $ 46.6万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001956&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Structures

Five investigators will study related problems involving various aspects of differential geometry, algebraic varieties, and dynamical systems. The first will study variational problems arising from curvature considerations. The second will study isospectral deformations, optimal structures on Riemannian manifolds, and fibrations of spheres by great spheres. The third will investigate Einstein metrics, isotropic irreducible Riemannian manifolds, and the isotropy representation of symmetric spaces. A topologist will study stratified spaces, particularly algebraic varieties. And the fifth will study hyperbolic geometry in higher dimensions, representations of braid groups, link groups, and invariant links. A central goal of the differential geometers working on this project is to understand spacial curvature. In particular they will study the relationship between curvature and the overall shape of the space, or what sorts of functions may exist on the space. The topologist and dynamical systems theorist will use their understanding of the shape of the space and allowable dynamical properties to restrict curvature in various ways.

五名研究人员将研究涉及微分几何、代数簇和动力系统的各个方面的相关问题。第一部分将研究由曲率因素引起的变分问题。第二部分将研究黎曼流形上的等谱变形、最优结构，以及大球面的球面纤化。第三部分将研究爱因斯坦度量、各向同性不可约黎曼流形和对称空间的各向同性表示。拓扑学家将研究分层空间，特别是代数簇。第五门课将学习高维双曲几何、辫子群、链环群和不变链环的表示。在这个项目中工作的微分几何仪的一个中心目标是了解空间曲率。特别是，他们将研究曲率和空间整体形状之间的关系，或者空间上可能存在什么样的功能。拓扑学家和动力系统理论家将利用他们对空间形状和允许的动力学性质的理解，以各种方式限制曲率。