Invariant Einstein metrics on generalized Wallach spaces
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摘要:
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.