Mathematical Sciences: Geometry of Surfaces in Lorentz Space

数学科学：洛伦兹空间中的曲面几何

• 批准号: 8802664
• 负责人: Martin Magid
• 金额: $ 3.77万
• 依托单位: Wellesley College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802664&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Surfaces; Lorentz

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.

马丁·马吉德将研究洛伦兹空间中的类时面和类空面。研究这些表面的主要动机来自物理学和广义相对论。他打算使用高斯图来更深入地了解这些表面。类时曲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。类空间曲面的高斯映射在洛伦兹空间的类空间二维平面的格拉斯曼范围内。Magid将研究这样一个表面在多大程度上是由它的高斯图决定的，以及哪些地图是高斯图。他还将考虑高斯图的像具有恒定曲率的曲面。他的第二个课题是研究平均曲率为零的类时曲面的分类，这些曲面以函数图的形式给出。