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Classification of invariant Einstein metrics on certain compact homogeneous spaces

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Abstract

In this paper, we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands. We show that, if G/K is a compact isotropy irreducible space with G and K simple, then except for some very special cases, the coset space G × G=Δ(K) carries at least two invariant Einstein metrics. Furthermore, in the case that G1;G2 and K are simple Lie groups, with K ⊂ G1;K ⊂ G2, and G1 ≠ G2, such that G1/K and G2/K are compact isotropy irreducible spaces, we give a complete classification of invariant Einstein metrics on the coset space G1 × G2=Δ(K).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11401425, 11626134, 11701300, 11671212 and 51535008) and K. C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo, 315211, China

    Zaili Yan

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

    Huibin Chen & Shaoqiang Deng

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  1. Zaili Yan
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Correspondence to Shaoqiang Deng.

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Yan, Z., Chen, H. & Deng, S. Classification of invariant Einstein metrics on certain compact homogeneous spaces. Sci. China Math. 63, 755–776 (2020). https://doi.org/10.1007/s11425-018-9357-1

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