Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Yukai Sun, East China Normal University, P.R. of China, Xianzhe Dai, UCSB, USA
2020 Symmetry, Integrability and Geometry: Methods and Applications  
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.
doi:10.3842/sigma.2020.068 fatcat:jwjzmwbx5vbjrc4hb4gyk45ra4