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

doi:10.1007/s10473-021-0315-x

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

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

张绍祥¹, 陈慧斌², 邓少强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. 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/Abstract

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

张绍祥, 陈慧斌, 邓少强. NEW NON-NATURALLY REDUCTIVE EINSTEIN METRICS ON Sp(n)[J]. 数学物理学报(英文版), 2021, 41(3): 887-898.

Shaoxiang ZHANG, Huibin CHEN, Shaoqiang DENG. NEW NON-NATURALLY REDUCTIVE EINSTEIN METRICS ON Sp(n)[J]. Acta mathematica scientia,Series B, 2021, 41(3): 887-898.

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

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

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