Mathematical Sciences: Research in Pseudo-Riemannian Geometry and Mathematical Relativity

数学科学：伪黎曼几何和数学相对论研究

• 批准号: 9006678
• 负责人: Gregory Galloway
• 金额: $ 3.5万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006678&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Pseudo; Riemannian

The principal investigator will study problems in Lorentzian, Riemannian, and pseudo-Riemannian geometry. He will build from his earlier work involving a Lorentzian analogue of the Cheeger-Gromoll splitting theorem of Riemannian geometry. This work will entail an analysis of the existence of timelike lines in space-times obeying suitable curvature, causality, and completeness conditions. In another vein, he will use minimal surface theory to demonstrate the simplicity of spacial topology near a black hole. Lastly, he will investigate as to whether compact pseudo-Riemannian manifolds have closed geodesics. The principal investigator will study several problems related to the geometry of space-time. Einstein was the first to suggest that the universe is a four-dimensional dynamic hypersurface which both restricts the movement of masses and is curved by their gravity. In this project, mathematics developed for the study of more general hypersurfaces will be applied to the specific hypersurfaces which are used to model our space- time.

首席研究员将研究问题， 洛伦兹几何、黎曼几何和伪黎曼几何。 他将 从他早期的工作中建立起来， 黎曼几何的Cheeger-Gromoll分裂定理 这项工作将需要分析类时 时空中的线服从适当的曲率，因果关系， 完备性条件 在另一种情况下，他将使用最小的 表面理论来证明空间拓扑的简单性 靠近黑洞。 最后，他将调查是否 紧伪黎曼流形有闭测地线。 首席研究员将研究几个问题 与时空的几何学有关。 爱因斯坦是第一个 认为宇宙是一个四维动力学 超曲面既限制了质量的运动， 被它们的引力弯曲。 在这个项目中，数学发展了 对于更一般的超曲面的研究将被应用于 用来模拟我们空间的特定超曲面 时间