Deformations of 3-dimensional cone-manifold structures

3维锥流管结构的变形

• 批准号: 5407518
• 负责人: Professor Dr. Hartmut Weiß
• 金额: --
• 依托单位: Mathematisches Seminar
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2005-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5407518?language=en
• 关键词: Deformations; dimensional; cone; manifold; structures

A 3-dimensional cone-manifold is a 3-manifold equipped with a singular geometric structure. More precisely, it carries a length metric, which is in the complement of a piecewise geodesic graph induced by a Riemannian metric of constant sectional curvature. On a disk transverse to an edge of the singular locus, the metric has an isolated conical singularity. One associates with each singular edge the cone-angle, which is a positive real number. This concept arises in the geometrization of 3-dimensional orbifolds, it can be considered as a natural generalization of the concept of geometric orbifold. The orbifold theorem, which was announced by W. Thurston in 1982 and recently proved by M. Boileau, B. Leeb and J. Porti in its general form, states that 3-manifolds with a certain kind of symmetry are geometrizable. ... I intend to study the following questions: Can these results be extended beyond cone-angle pi in the graph-case? Is a global rigidity theorem available? What can be said in the Euclidean case?

3维锥体模型是配备奇异几何结构的3个manifold。更确切地说，它带有长度度量，该度量是由恒定截面曲率的riemannian度量诱导的分段测量图的补充。在横向到奇异基因座边缘的磁盘上，公制具有孤立的圆锥形奇异性。一个人与每个奇异的边缘相关联，这是一个积极的实际数字。这个概念出现在三维轨道的几何化中，它可以被认为是几何轨道概念的自然概括。 Orbifold定理由W. Thurston于1982年宣布，最近由M. Boileau，B。Leeb和J. Porti以其一般形式证明，并指出，具有某种对称性的3个模型可几何。 ...我打算研究以下问题：这些结果是否可以扩展到图形案例中的锥角pi之外？全球刚度定理吗？在欧几里得案中可以说什么？