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arXiv · 2005.00161

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

Yukai Sun·Xianzhe Dai
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Abstract

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.

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Yukai Sun, Xianzhe Dai. 2020-05-01. Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces. https://doi.org/10.3842/sigma.2020.068

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