Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 887-898.doi: 10.1007/s10473-021-0315-x

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Shaoxiang ZHANG1, Huibin CHEN2, Shaoqiang DENG1   

  1. 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
    2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
  • Received:2020-01-05 Revised:2020-10-27 Online:2021-06-25 Published:2021-06-07
  • Contact: Shaoqiang DENG
  • About author:Shaoxiang ZHANG,;Huibin CHEN,
  • Supported by:
    This work was supported by NSFC (12071228, 11901300, 51535008) and Natural Science Research of Jiangsu Education Institutions of China (19KJB110015).

Abstract: In this paper, we consider a class of left invariant Riemannian metrics on Sp(n), which is invariant under the adjoint action of the subgroup Sp(n-3)×Sp(1)×Sp(1)×Sp(1). Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gröbner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.

Key words: Einstein metric, non-naturally reductive metric, compact Lie group, symplectic group

CLC Number: 

  • 53C25