论文标题
lie群和均匀空间上双重不变的指标的刚性刚度
Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces
论文作者
论文摘要
格罗莫夫（Gromov）询问与其他任何指标相比，紧凑型谎言组上的双重视指标是否是极端的。在本说明中，我们证明，与左右不变的指标相比，在Gromov的意义上，紧凑型连接的半简单谎言组$ g $的双重不变指标是极端的。实际上，与$ g $紧凑的连接和半简单的紧凑型连接的均匀歧管$ g/h $相同的结果。
Gromov asked if the bi-invariant metrics on a compact Lie group are extremal compared to any other metrics. In this note, we prove that the bi-invariant metrics on a compact connected semi-simple Lie group $G$ are extremal (in fact rigid) in the sense of Gromov when compared to the left-invariant metrics. In fact the same result holds for a compact connected homogeneous manifold $G/H$ with $G$ compact connect and semi-simple.
