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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Sun, Yukai, Dai, Xianzhe
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210780
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces. Yukai Sun and Xianzhe Dai. SIGMA 16 (2020), 068, 6 pages

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 met...