Mathematical Sciences: Research in Pseudo-Riemannian Geometry

数学科学：伪黎曼几何研究

• 批准号: 8802877
• 负责人: Gregory Galloway
• 金额: $ 4.43万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802877&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Pseudo; Riemannian

Gregory Galloway will continue his studies of Lorentzian geometry. This is an area which overlaps both physics and mathematics. The study of events from a relativistic point of view leads to different invariants which in turn result in the study of different notions of distance, called Lorentzian metrics. The geometric phenomena to be studied are related to singularities in relativistic space time. Galloway will try to obtain further results building on his recent progress on the splitting theorem. The physical motivation for this work is the study of rigidity phenomena in the arena of singularity theory of general relativity. He will also study problems related to the existence of closed geodesics in pseudo- Riemannian manifolds. These are known to exist in compact Riemannian manifolds. Galloway will try to use a dynamic approach to the case where the metric is indefinite.

格雷戈里·加洛韦将继续他对洛伦兹的研究 几何这是一个与物理学和 数学从相对论的角度对事件的研究 视图导致不同的不变量，这反过来又导致 研究不同的距离概念，称为洛伦兹 指标.要研究的几何现象与 相对论时空中的奇点 加洛韦将努力在他的基础上取得进一步的成果。 分裂定理的最新进展物理动机 因为这项工作是研究刚性现象的竞技场， 广义相对论的奇点理论他还将研究 关于伪空间中闭测地线的存在性问题， 黎曼流形已知它们存在于 黎曼流形加洛韦将尝试使用动态方法 对于度量不确定的情况。