论文标题
在均匀的三维空间上：关注飞机波
On homogeneous 3-dimensional spacetimes: focus on plane waves
论文作者
论文摘要
我们重新审视lorentz同质空间的分类$ 3 $，并放松通常的完整假设。特别是，在$ 3 $维的Lie group上，非偏椭圆形波和只有它们既不是局部对称的，也不是局部等距的局部等距。我们在尺寸$ 3 $中表征同质的平面波，并证明它们是不可扩展的，并且只有在对称的情况下才能完成。最后，只有一个非平面波有一个紧凑的模型。
We revisit the classification of Lorentz homogeneous spaces of dimension $3$, and relax usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmetric nor locally isometric to a left-invariant Lorentz metric on a $3$-dimensional Lie group. We characterize homogeneous plane waves in dimension $3$, and prove they are non-extendable, and geodesically complete only if they are symmetric. Finally, only one non-flat plane wave has a compact model.
