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Invariant Einstein metrics on generalized Wallach spaces

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Abstract

Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l + m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type SO(k+l+m)/SO(k) × SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety.

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Acknowledgements

This work was supported by Ministry of Education and Sciences of the Republic of Kazakhstan for 2015–2017 (Agreement N 299, February 12, 2015) (Grant No. 1452/GF4). The authors are grateful to the referees for helpful comments and suggestions that improved the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Zhiqi Chen

  2. Southern Mathematical Institute of Vladikavkaz Scientific Centre of the Russian Academy of Sciences, Vladikavkaz, 362027, Russia

    Yuriĭ Gennadievich Nikonorov

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  1. Zhiqi Chen
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  2. Yuriĭ Gennadievich Nikonorov
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Correspondence to Zhiqi Chen.

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Chen, Z., Nikonorov, Y.G. Invariant Einstein metrics on generalized Wallach spaces. Sci. China Math. 62, 569–584 (2019). https://doi.org/10.1007/s11425-017-9150-3

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  • DOI: https://doi.org/10.1007/s11425-017-9150-3

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