数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 887-898.doi: 10.1007/s10473-021-0315-x

• 论文 • 上一篇    下一篇

NEW NON-NATURALLY REDUCTIVE EINSTEIN METRICS ON Sp(n)

张绍祥1, 陈慧斌2, 邓少强1   

  1. 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;
    2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
  • 收稿日期:2020-01-05 修回日期:2020-10-27 出版日期:2021-06-25 发布日期:2021-06-07
  • 通讯作者: Shaoqiang DENG E-mail:dengsq@nankai.edu.cn
  • 作者简介:Shaoxiang ZHANG,E-mail:zhangshaoxiang@mail.nankai.edu.cn;Huibin CHEN,E-mail:chenhuibin@mail.nankai.edu.cn
  • 基金资助:
    This work was supported by NSFC (12071228, 11901300, 51535008) and Natural Science Research of Jiangsu Education Institutions of China (19KJB110015).

NEW NON-NATURALLY REDUCTIVE EINSTEIN METRICS ON Sp(n)

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 E-mail:dengsq@nankai.edu.cn
  • About author:Shaoxiang ZHANG,E-mail:zhangshaoxiang@mail.nankai.edu.cn;Huibin CHEN,E-mail:chenhuibin@mail.nankai.edu.cn
  • Supported by:
    This work was supported by NSFC (12071228, 11901300, 51535008) and Natural Science Research of Jiangsu Education Institutions of China (19KJB110015).

摘要: 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.

关键词: Einstein metric, non-naturally reductive metric, compact Lie group, symplectic group

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

中图分类号: 

  • 53C25