论文标题
对空间形式和罗伯逊 - 步行者的几何形状研究 - 概述
A geometric study of marginally trapped surfaces in space forms and Robertson-Walker spacetimes -- an overview
论文作者
论文摘要
时空中略微捕获的表面是riemannian表面，其平均曲率矢量在每个点都呈浅色。在本文中，我们对Minkowski，de Sitter，Anti-De保姆和Robertson-Walker SpaceTimes的这些表面的微分几何研究进行了最新概述。 We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical.最后，我们提供了持续的高斯曲率略微捕获的表面并提出一些空旷问题的示例。
A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and Robertson-Walker spacetimes. We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical. Finally, we provide examples of constant Gaussian curvature marginally trapped surfaces and state some open questions.
