满旗流形SO(8)/T上不变爱因斯坦度量（英文）  

INVARIANT EINSTEIN METRICS ON FULL FLAG MANIFOLD OF SO(8)/T

作　　者：王瑜[1,2] 李天增[1,2] 

机构地区：[1]四川理工学院理学院,四川自贡643000 [2]四川理工学院桥梁无损检测与工程计算四川省高校重点实验室,四川自贡643000

出　　处：《数学杂志》2015年第6期1319-1328,共10页Journal of Mathematics

基　　金：Supported by Sichuan University of Science and Engineering grant(2012PY17);Sichuan Province University Key Laboratory of Bridge Non-Destruction Detecting and Engineering Computing grant(2014QZJ03);Partially Supported by Scientific Research Fund of Sichuan Province Education Department Grant(15SB0122)

摘　　要：本文研究了迷向表示分为12个不可约子空间的满旗流形SO(8)/T上不变爱因斯坦度量的问题.利用计算机计算满旗流形SO(8)/T爱因斯坦方程组的方法,得到了满旗流形SO(8)/T上有160个不变爱因斯坦度量(up to a scale)的结果,在等距情况下考虑这160个不变爱因斯坦度量,其中1个是凯莱爱因斯坦度量,4个是非凯莱爱因斯坦度量.推广了只对迷向表示分为小于等于6个不可约子空间的满旗流形上不变爱因斯坦度量的研究.We consider the problem of the invariant Einstein metrics on the full flag manifolds M = SO（8）/T with twelve isotropy summands.With the help of the computer we obtain there are one hundred and sixty invariant Einstein metrics（up to a scale） on the full flag manifold of SO（8）/T,of which one is K¨ahler Einstein metric（up to isometry） and four are non-K¨ahler Einstein metrics（up to isometry）.We promote the original methods which are applied to the full flag manifolds with not more than six isotropy summands.

关 键 词：满旗流形 爱因斯坦度量 RICCI张量 迷向表示 

分 类 号：O186.14[理学—数学]