Geodesic
New Einstein metrics on ${\rm Sp}(n)$ which are non-naturally reductive
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 349-363

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We prove that there are at least two new non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics on ${\rm Sp} (l+3k)$ $(k l)$. It implies that every compact simple Lie group ${\rm Sp} (n)$ for $n= l+3k>4$ admits at least $2[\tfrac 14 (n-1)]$ non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics.
DOI : 10.21136/CMJ.2021.0491-20
Classification : 53C25, 53C30, 65H10
Keywords: Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group 
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Zhang, Shaoxiang; Chen, Huibin. New Einstein metrics on ${\rm Sp}(n)$ which are non-naturally reductive. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 2, pp. 349-363. doi: 10.21136/CMJ.2021.0491-20

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