Crooked Halfspaces
Crooked Halfspaces
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弯曲的半场
DOI：
10.4171/lem/60-1/2-4
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发表时间：
2012
影响因子：
0.6
通讯作者：
W. Goldman
中科院分区：
文献类型：
--
作者：
Jean;Virginie Charette;Todd A. Drumm;W. Goldman
我们在 2 + 1 维 Minkowski 空间中开发了弯曲半空间的洛伦兹几何。我们计算弯曲半空间的仿射、共形和等距自同构群，并讨论其轨道类型的分层，给出自同构群作用的显式切片。弯曲半空间中的类时线或粒子的平行类集合是双曲平面中的测地线半平面。开放弯曲半空间中的每个点都位于一个粒子上。双曲 2 空间中弯曲半空间和半平面之间的对应关系保留了包含定义的偏序和互补定义的对合。我们找到了粒子完全位于弯曲半空间中的条件。我们根据保留弯曲半空间的平移半群重新审视由 Drumm 和 Goldman 开发的弯曲平面的不相交准则。然后将这些想法应用于通过弯曲平面来描述闵可夫斯基空间的叶状结构。日期：2014年5月5日。2000年数学学科分类。 53B30（洛伦兹度量，不定度量），53C50（洛伦兹流形，具有不定度量的流形）。
We develop the Lorentzian geometry of a crooked halfspace in 2 + 1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types, giving an explicit slice for the action of the automorphism group. The set of parallelism classes of timelike lines, or particles, in a crooked halfspace is a geodesic halfplane in the hyperbolic plane. Every point in an open crooked halfspace lies on a particle. The correspondence between crooked halfspaces and halfplanes in hyperbolic 2-space preserves the partial order defined by inclusion, and the involution defined by complementarity. We find conditions for when a particle lies completely in a crooked half space. We revisit the disjointness criterion for crooked planes developed by Drumm and Goldman in terms of the semigroup of translations preserving a crooked halfspace. These ideas are then applied to describe foliations of Minkowski space by crooked planes. Date: May 5, 2014. 2000 Mathematics Subject Classification. 53B30 (Lorentz metrics, indefinite metrics), 53C50 (Lorentz manifolds, manifolds with indefinite metrics).