具有平坦的不变伪度量的李群

Lie Groups With Flat Invariant Pseudo-Riemannian Metrics

设Ｇ为具有不变伪度量的李群，本文给出了Ｇ平坦的一些条件，当度量的指标小于３时，证明了Ｇ平坦的充要条件是Ｇ可换，由此确定了维数小于６的平坦李群，最后举例说明了存在不可换的平坦李群。

Let G be Lie groups equipped With a invariant pseudo-riemannian metric .This paper pre-sents some conditions under which G is flat.When the index of the metric is less than 3. it provesthat G is flat if and only if G is Abel. So if dimG<6.G is Abel.At last the paper gives a non-A-belean flat Lie group.