Extremality of Bi-invariant Metrics on Lie Groups and Homogeneous Spaces [article]

Yukai Sun, Xianzhe Dai
2020 arXiv   pre-print
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 compact connected semi-simple Lie group G is extremal in the sense of Gromov when compared to the left invariant metrics. In fact the same result holds for a compact connected homogeneous Riemannian manifold G/H with the Lie algebra of G having trivial center.
arXiv:2005.00161v2 fatcat:qak36iqilvapfk5u25yzf3tpiy