Curvature, geodesics, and rigidity

曲率、测地线和刚度

• 批准号: 1207655
• 负责人: Benjamin Schmidt
• 金额: $ 14.97万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207655&HistoricalAwards=false
• 关键词: Curvature; geodesics; rigidity

AbstractAward: DMS 1207655, Principal Investigator: Benjamin SchmidtThe principal investigator will study the rigidity and deformation properties of curvature and geodesics in Riemannian manifolds. A specific goal is to classify the Riemannian manifolds having all sectional curvatures greater than or equal to one and with positive spherical rank. Conjecturally, these manifolds are isometric to compact rank one symmetric spaces. Another broad goal is to investigate the structure of constant vector curvature manifolds in dimensions four and higher.Objects in nature with a high degree of symmetry are quite often structurally rigid. When highly symmetric spaces are altered, numerical measurements of the way light propagates and the way space bends can be used to quantify changes. The principal investigator will study the influence of Riemannian curvature, a numerical measurement of bending, on the way that highly symmetric spaces can and cannot be perturbed.

AbstractAward：DMS 1207655，首席研究员：本杰明·施密特首席研究员将研究黎曼流形中曲率和测地线的刚性和变形性质。 一个具体的目标是分类黎曼流形的所有截面曲率大于或等于一，并与积极的球秩。 猜想，这些流形是等距紧秩一对称空间。 另一个广泛的目标是研究四维及更高维的常向量曲率流形的结构。自然界中具有高度对称性的物体在结构上往往是刚性的。 当高度对称的空间被改变时，光传播方式和空间弯曲方式的数值测量可以用来量化变化。 主要研究者将研究黎曼曲率的影响，弯曲的数值测量，对高度对称空间可以和不能扰动的方式。