Homogeneous Einstein-like metrics on symmetric spaces

Chao Qian; An Wu

doi:10.1007/s11425-019-9744-0

Homogeneous Einstein-like metrics on symmetric spaces

Chao Qian, An Wu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M, which is not isometric to a compact Lie group and has rank greater than 1. Whenever there exists a closed proper subgroup G′ of G = Isom₀(M) acting transitively on M, we find all G′-invariant A-metrics and ℬ-metrics on M. More precisely, we prove that G′-invariant metrics on M must be A-metrics, and G′-invariant ℬ-metrics on M are always Einstein.

Original language	English
Pages (from-to)	1045-1060
Number of pages	16
Journal	Science China Mathematics
Volume	64
Issue number	5
DOIs	https://doi.org/10.1007/s11425-019-9744-0
Publication status	Published - May 2021

Keywords

53C25
53C30
A-metric
Einstein-like metric
homogeneous space
symmetric space
ℬ-metric

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10.1007/s11425-019-9744-0

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keywords = "53C25, 53C30, A-metric, Einstein-like metric, homogeneous space, symmetric space, ℬ-metric",

author = "Chao Qian and An Wu",

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AB - In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M, which is not isometric to a compact Lie group and has rank greater than 1. Whenever there exists a closed proper subgroup G′ of G = Isom0(M) acting transitively on M, we find all G′-invariant A-metrics and ℬ-metrics on M. More precisely, we prove that G′-invariant metrics on M must be A-metrics, and G′-invariant ℬ-metrics on M are always Einstein.

KW - 53C25

KW - 53C30

KW - A-metric

KW - Einstein-like metric

KW - homogeneous space

KW - symmetric space

KW - ℬ-metric

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JF - Science China Mathematics

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Homogeneous Einstein-like metrics on symmetric spaces

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Keywords

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