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

Autor:	Xianzhe Dai, Yukai Sun
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Pure mathematics 010102 general mathematics Lie group 01 natural sciences Differential Geometry (math.DG) Homogeneous FOS: Mathematics Geometry and Topology 0101 mathematics Invariant (mathematics) Mathematical Physics Analysis Mathematics Scalar curvature
Zdroj:	Symmetry, Integrability and Geometry: Methods and Applications.
ISSN:	1815-0659
DOI:	10.3842/sigma.2020.068
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77e27ca34589d6da7916038a16b94a3d https://doi.org/10.3842/sigma.2020.068 Zobrazit plný text záznamu