广义旗流形上的齐型爱因斯坦度量

摘要

利用MATHEMATICA 里的Nsolve命令计算出满旗流形 G2/T在差常数倍的情况下有十二个G-不变的爱因斯坦度量，其中六个是Kähler爱因斯坦度量，六个非Kähler爱因斯坦度量。同样用此方法可计算出旗流形 E（8）/U（1）× SU（2）× SU（3）× SU（5）的爱因斯坦方程组有五个正实数解，其中一个是Kähler 爱因斯坦度量，四个非Kähler 爱因斯坦度量。%By using MATHEMATICA we get all the twelve positive real solutions (up to a scale) of the system of Einstein equations for the flag manifold G2/T ,of w hich six are Kähler Einstein metrics and six are non-Kähler Einstein metrics .Then we get the positive solutions (up to a scale ) for the system of Einstein equations for the flag manifold E(8)/U(1)× SU(2)× SU(3)× SU(5)by using MATHEMATI-CA ,then we obtain that there are five G-invariant Einstein metrics (up to a scale ) for the flag manifold E(8)/U(1) × SU(2) × SU(3) × SU(5) ,of which one is Kähler Einstein metric and four are non-Kähler Einstein metrics .