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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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
Keywords
- compact homogeneous space
- generalized Wallach space
- symmetric space
- homogeneous Riemannian metric
- Einstein metric
- Ricci flow