Extremality of Bi-invariant Metrics on Connected Semi-simple Lie Groups

Gromov asked if the bi-invariant metric on an $n$ dimensional compact Lie group is extremal compared to any other metrics. In this note, we prove that the bi-invariant metric on an $n$ dimensional connected semi-simple Lie group $G$ is extremal in the sense of Gromov when compared to the left invariant metrics.