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Homogeneous Einstein-like metrics on symmetric spaces

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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 \({\mathcal A}\)-metrics and \({\mathcal B}\)-metrics on M. More precisely, we prove that G′-invariant metrics on M must be \({\mathcal A}\)-metrics, and G′-invariant \({\mathcal B}\)-metrics on M are always Einstein.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871282, 11571339 and 11401560). The authors are greatly indebted to Professor Chiakuei Peng for the guidance over the past years, and are grateful to Professor Huafei Sun for his consistent encouragement.

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  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 102488, China

    Chao Qian & An Wu

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  1. Chao Qian
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  2. An Wu
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Correspondence to An Wu.

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Qian, C., Wu, A. Homogeneous Einstein-like metrics on symmetric spaces. Sci. China Math. 64, 1045–1060 (2021). https://doi.org/10.1007/s11425-019-9744-0

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  • DOI: https://doi.org/10.1007/s11425-019-9744-0

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