Mathematical Sciences: Geometry of Surfaces in Lorentz Space

马丁·马吉德将研究洛伦兹空间中的类时和类空表面。研究这些表面的主要动机来自物理学和广义相对论。他打算使用高斯贴图来实现对这些曲面的更深层次的理解。类时表面可以用来构造时空，并通过提供低维的例子来理解时空的几何结构。类空曲面的高斯映射的值域是洛伦兹空间中类空二维平面的Grassman映射。MAGID将调查这样的表面在多大程度上由其高斯贴图决定，以及哪些贴图是高斯贴图。他还将考虑高斯映射的图像具有常曲率的曲面。他的第二个项目是关于平均曲率为零的类时曲面的分类，这些类时曲面是作为函数的图形给出的。

Martin Magid will investigate timelike and spacelike surfaces in Lorentz space. The primary motivation for studying these surfaces comes from physics and the theory of general relativity. He intends to use the Gauss map to achieve a deeper understanding of these surfaces. Timelike surfaces can be used to construct spacetimes and to understand the geometry of spacetimes by providing lower dimensional examples. The Gauss map of a spacelike surface has its range in the Grassmannian of spacelike two dimensional planes in Lorentz space. Magid will investigate to what extent such a surface is determined by its Gauss map and which maps are Gauss maps. He will also consider surfaces for which the image of the Gauss map has constant curvature. His second project is concerned with the classification of timelike surfaces with zero mean curvature which are given as the graph of a function.