Conformal Geometry of semi-Riemannian Manifolds

半黎曼流形的共形几何

• 批准号: 5453380
• 负责人: Professor Dr. Hans-Bert Rademacher
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5453380?language=en
• 关键词: Conformal; Geometry; semi; Riemannian; Manifolds

Conformal Symmetries have been studied in General Relativity during many decades, and many concepts in differential geometry and mathematical physics are conformally invariant. In dimension four vacuum spacetimes with non-trivial conformal symmetries are pp-metrics first introduced by Brinkmann. We plan to introduce an extension of pp-metrics (which we call generalized Brinkmann spaces) and study the following questions in the two parts of our project:1. Conformal Symmetries of Generalized Brinkmann Spaces For an appropriate generalization of pp-metrics including pure radiation metrics with a lightlike Killing field we study conformal symmetries and conformal transformations inside the class of these metrics.2. Spin-Geometry of Generalized Brinkmann Spaces We plan to study conformal compactifications of pp-metrics resp. generalized Brinkmann spaces admitting twistor spinors with zeros. Another line of investigation will be concerned with solutions of generalized Killing spinor equations and the construction of supersymmetries.

广义相对论对共形对称性的研究已有几十年的历史，微分几何和数学物理中的许多概念都是共形不变的。在四维空间中，具有非平凡保角对称的真空时空是由Brinkmann首先提出的pp度规。我们计划引入pp度量的一个扩展(我们称之为广义Brinkmann空间)，并在项目的两个部分中研究以下问题：1.广义Brinkmann空间的共形对称性为了适当地推广pp度量，包括具有类光杀伤场的纯辐射度量，我们研究了这些度量类内的共形对称和共形变换。广义Brinkmann空间的自旋几何我们计划分别研究pp-度量的共形紧化。广义Brinkmann空间允许有零的扭曲旋量。另一项研究将涉及广义Killing旋量方程的解和超对称的构造。