论文标题
最大的简单将洛伦兹表面与杀戮场及其完整性相连
Maximal simply connected Lorentzian surfaces with a Killing field and their completeness
论文作者
论文摘要
在本文的第一部分中，我们对简单连接的最大Lorentzian表面进行了全局描述，其异构体为尺寸1（即完全杀死场），就一维通常非Hausdorff歧管（杀死孔的空间）而言，且函数定义为平滑的功能。在第二部分中，我们研究了此类表面的完整性，并特别证明，在有界曲率的假设下，完整性等于无效。我们还提供涉及杀死轨道空间的拓扑结构的完整标准，或该空间的拓扑和表面的几何形状。
In the first part of this paper, we give a global description of simply connected maximal Lorentzian surfaces whose group of isometries is of dimension 1 (i.e. with a complete Killing field), in terms of a 1-dimensional generally non-Hausdorff manifold (the space of Killing orbits) and a smooth function defined there. In the second part, we study the completeness of such surfaces and prove in particular that under the hypothesis of bounded curvature, completeness is equivalent to null completeness. We also give completeness criterions involving the topological structure of the space of Killing orbits, or both the topology of this space and the geometry of the surface.
