兰州理工大学学报

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (1): 164-172.

• 数理科学 • 上一篇    

满旗流形Sp(3)/T的不变爱因斯坦度量

高莹莹, 王瑜*   

  1. 四川轻化工大学 数学与统计学院, 四川 自贡 643000
  • 收稿日期:2021-12-01 出版日期:2023-02-28 发布日期:2023-03-21
  • 通讯作者: 王 瑜(1980-),女,河南漯河人,教授. Email:wangyu_813@163.com
  • 基金资助:
    四川省科技厅项目(2021ZYD0004)

The invariant Einstein metrics of the full flag manifold Sp(3)/T

GAO Ying-ying, WANG Yu   

  1. School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000
  • Received:2021-12-01 Online:2023-02-28 Published:2023-03-21

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摘要： 研究了迷向表示分为9个不可约子空间的满旗流形Sp(3)/T上的不变爱因斯坦度量,计算Sp(3)/T非零结构常数的值,根据其爱因斯坦方程,利用Maple软件得到64个不变爱因斯坦度量(差常数倍的情况下),在等距的意义下,其中有1个凯莱爱因斯坦度量和3个非凯莱爱因斯坦度量.

关键词: 广义旗流形, 迷向表示, 爱因斯坦度量, 等距

Abstract: The invariant Einstein metrics of the full flag manifold Sp(3)/T that was divided into nine isotropy subspaces were studied. First, the value of the non-zero structure constant was calculated, then according to its Einstein equation, sixty-four invariant Einstein metrics (up to a scale) were obtained by the Maple, which included a unique Kähler Einstein metric and three non-Kähler Einstein metrics (up to isometry) in the sense of equidistance.

Key words: generalized flag manifold, isotropy representation, Einstein metric, isometry

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