Invariant Einstein metrics on generalized Wallach spaces
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 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 Einstein invariant metrics up to a homothety.
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