Czechoslovak Mathematical Journal, Vol. 72, No. 2, pp. 349-363, 2022
New Einstein metrics on Sp$(n)$ which are non-naturally reductive
Shaoxiang Zhang, Huibin Chen
Received November 11, 2020. Published online July 29, 2021.
Abstract: 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 $2[\tfrac14 (n-1)]$ non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times{\rm Sp}(k)\times{\rm Sp}(k)\times{\rm Sp}(k))$ invariant Einstein metrics.
Keywords: Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group
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Affiliations: Shaoxiang Zhang, College of Mathematics and System Science, Shandong University of Science and Technology, 579 Qianwangang Road, Huangdao District, Qingdao, Shandong Province, 266590, P. R. China, e-mail: zhangshaoxiang@mail.nankai.edu.cn; Huibin Chen (corresponding author), School of Mathematical Sciences, Nanjing Normal University, 1 Wenyuan Rd, Qixia, Nanjing, Jiangsu, 210023, P. R. China, e-mail: chenhuibin@njnu.edu.cn
