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A complete classification of left-invariant Einstein metrics on $S^3\times S^3$
We complete the classification of compact simply connected homogeneous Einstein manifolds in dimension six by resolving the remaining cases for left-invariant Einstein metrics on $G=\mathrm{SU}(2)\times\mathrm{SU}(2)\cong S^3\times S^3$. Previous work leaves two cases for the isotropy group $K$, nam
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