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arXiv · 1511.02567

Invariant Einstein metrics on generalized Wallach spaces

Zhiqi Chen·Yu. G. Nikonorov
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Abstract

Invariant Einstein metrics on generalized Wallach spaces have been classified except $SO(k+l+m)/SO(k)\times SO(l)\times SO(m)$. In this paper, we 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 $SO(k+l+m)/SO(k)\times SO(l)\times SO(m)$ admitting exactly two, three, or four Einstein invariant metrics up to a homothety.

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Zhiqi Chen, Yu. G. Nikonorov. 2015-11-09. Invariant Einstein metrics on generalized Wallach spaces. https://doi.org/10.1007/s11425-017-9150-3

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