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| 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. |
| 关键词: 满旗流形 爱因斯坦度量 Ricci张量 迷向表示 |
| DOI： |
| 分类号:O186.14 |
| 基金项目:Supported by Sichuan University of Science and Engineering grant (2012PY17); Sichuan Province University Key Laboratory of Bridge Non-Destruction Detecting and Engineering Com-puting grant (2014QZJ03); Partially Supported by Scientific Research Fund of Sichuan Province Educa-tion Department Grant (15SB0122). |
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| INVARIANT EINSTEIN METRICS ON FULL FLAG MANIFOLD OF SO(8)=T |
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WANG Yu,LI Tian-zeng
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| Abstract: |
| 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 Kähler Einstein metric (up to isometry) and four are non-Kähler 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. |
| Key words: full flag manifold Einstein metric Ricc tensor isotropy representation |
