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

首席研究员将研究洛伦兹几何、黎曼几何和伪黎曼几何中的问题。他将建立在他早期工作的基础上，涉及到黎曼几何中契格-格罗莫尔分裂定理的洛伦兹类比。这项工作将需要分析时空中服从适当曲率、因果关系和完备性条件的类时线的存在性。另一方面，他将使用最小表面理论来证明黑洞附近空间拓扑结构的简单性。最后，他将研究紧致伪黎曼流形是否具有闭合测地线。首席研究员将研究几个与时空几何有关的问题。爱因斯坦是第一个提出宇宙是一个四维动态超表面的人，它既限制了质量的运动，又被它们的引力弯曲。在这个项目中，为研究更一般的超曲面而开发的数学将应用于用于建模我们的时空的特定超曲面。

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.