Crooked surfaces and anti-de Sitter geometry
Crooked surfaces and anti-de Sitter geometry
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弯曲表面和反德西特几何形状
DOI：
10.1007/s10711-014-0034-8
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发表时间：
2013
影响因子：
0.5
通讯作者：
W. Goldman
中科院分区：
文献类型：
--
作者：
W. Goldman
弯曲平面由Drumm定义，用于约束马古利斯时空闵可夫斯基空间中的基本多面体。它们被Frances推广到闵可夫斯基空间（爱因斯坦空间）的共形紧化中的封闭多面体曲面，我们称之为弯曲曲面。反德西特空间的共形模型是通过一个固定爱因斯坦平面的对合得到的爱因斯坦空间商的内部。本文的目的是证明最近由danciger - gu<s:1>里道德-卡塞尔在反德西特空间中定义的弯曲平面对爱因斯坦空间中弯曲曲面的限制的提升，这些曲面是在定义反德西特空间的爱因斯坦空间的对合下适应的。
Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we call crooked surfaces. The conformal model of anti-de Sitter space is the interior of the quotient of Einstein space by an involution fixing an Einstein plane. The purpose of this note is to show that the crooked planes defined in anti-de Sitter space recently by Danciger-Guéritaud-Kassel lift to restrictions of crooked surfaces in Einstein space which are adapted under the involution of Einstein space defining anti-de Sitter space.