| 王瑜,秦华军,赵国松.迷向表示分为6个不可约直和的旗流形上不变爱因斯坦度量[J].数学年刊A辑,2019,40(3):259~286 |
| 迷向表示分为6个不可约直和的旗流形上不变爱因斯坦度量 |
| Invariant Einstein Metrics on Some Generalized Flag Manifolds with Six Isotropy Summands |
| Received:July 08, 2017 Revised:August 27, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0021 |
| 中文关键词: Homogeneous space, Generalized f/lag manifold, Software Maple, Isotropy representation, Einstein metric, Isometry |
| 英文关键词:Homogeneous space, Generalized f/lag manifold, Software Maple, Isotropy representation, Einstein metric, Isometry |
| 基金项目: |
| Author Name | Affiliation | E-mail | | WANG Yu | Corresponding author. Department of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China. | wangyu_813@163.com | | QIN Huajun | Department of Mathematics, Sichuan Normal University, Chengdu 610068, China. | qinhj028@sina.com | | ZHAO Guosong | Department of Mathematics, Sichuan University, Chengdu 610064, China. | qinhj028@sina.com |
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| 中文摘要: |
| 众所周知, 计算广义旗流形 $G/K$ 上不变爱因斯坦度量存在两个困难: (1) 如何计算旗流形的非零结构常数;
(2) 如何计算旗流形爱因斯坦方程组的Gr\"obner 基. 在这篇文章中用定理\ref{T2}来计算旗流形的非零结构常数,
用Maple软件来计算旗流形爱因斯坦方程组的 Gr\"obner 基. 最后得到旗流形
$F_4/U^2(1)\times SU(3), \ E_6/ U^2(1)\times SU(3)\times SU(3), \ E_7/ U^2(1)\times SU(2)\times SU(5),
\ E_7/ U^2(1)\times SU(6), \ E_7/U^2(1)\times SU(2)\times SO(8)$
与$E_8/ U^2(1)\times E_6$ 上爱因斯坦度量. |
| 英文摘要: |
| There are two difficulties to obtain
invariant Einstein metrics on generalized f\/lag manifolds $G/K$, one
is how to compute non-zero structure constants of the f\/lag
manifolds, the other is how to compute Gr\"obner bases of the
system of the Einstein equations. In this paper, the authors compute
non-zero structure constants by the method given in Theorem
\ref{T2}, and get Gr\"obner bases of the system of the Einstein
equations by using the software Maple. In this way the authors obtain
invariant Einstein metrics on the f\/lag manifolds
$F_4/U^2(1)\times SU(3)$, $E_6/ U^2(1)\times SU(3)\times SU(3)$,
$E_7/ U^2(1)\times SU(2)\times SU(5)$, $E_7/ U^2(1)\times
SU(6)$, $E_7/U^2(1)\times SU(2)\times SO(8)$ and $E_8/ U^2(1)\times
E_6$ respectively. |
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