论文标题
在某些Nilpotent Lie群体上对左转洛伦兹的分类
A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups
论文作者
论文摘要
众所周知，恰好存在三个左右的洛伦兹指标，直到三维的海森伯格集团上的缩放和自动形态。在本文中，我们将左右不变的Lorentzian指标与三维的海森堡集团的直接产品和欧几里得空间的直接乘积和$ n \ geq 4 $进行了分类，并证明了这个谎言组上的六个这样的指标，可以进行缩放和自动形态。此外，我们表明其中只有一个是平坦的，而其他五个指标是Ricci Solitons，而不是Einstein。我们还将这个平面度量表征为独特的封闭轨道，在该轨道上，可以用某个对称空间的某个组动作的轨道来识别每个左右不变度量的等效类别。
It has been known that there exist exactly three left-invariant Lorentzian metrics up to scaling and automorphisms on the three dimensional Heisenberg group. In this paper, we classify left-invariant Lorentzian metrics on the direct product of three dimensional Heisenberg group and the Euclidean space of dimension $n-3$ with $n \geq 4$, and prove that there exist exactly six such metrics on this Lie group up to scaling and automorphisms. Moreover we show that only one of them is flat, and the other five metrics are Ricci solitons but not Einstein. We also characterize this flat metric as the unique closed orbit, where the equivalence class of each left-invariant metric can be identified with an orbit of a certain group action on some symmetric space.
