广义旗流形SU(5)/U^3(1)×SU(2)齐性变爱因斯坦度量（英文）

New Homogeneous Einstein Metrics on the Generalized Flag Manifold SU(5)/U^3(1)×SU(2)

利用李代数的知识可以计算旗流形M=SU(5)/U3(1)×SU(2)上非零的结构常数ck ij,然后把非零的ck ij代入Ricc张量的分量γ1,…,γ6.旗流形M上G-不变的黎曼度量g是爱因斯坦度量当且仅当存在正常数e,使得γ1=γ2=γ3=γ4=γ5=γ6=e.利用计算Grbner基的方法得到爱因斯坦方程组有27个正的实数解,即广义旗流形M=SU(5)/U3(1)×SU(2)上有27个不变的爱因斯坦度量(在差常数倍的情况下),其中12个是凯莱爱因斯坦度量,15个是非凯莱爱因斯坦度量.

By the Lie theory we compute the non zero structure constants ckij of the generalized flag manifold of M =SU（5）/U3 （1） × SU（2）,then we substitute c,kij into the components γ1,…,γ6 of the Ricc tensor.We know that a G -invariant Riemmanian metric g on M is Einstein if and only if there is a positive constant e such that γ1-γ2-γ3 =γ4 =γ5 =γ6 =e.We obtain twenty-seven positive solutions by computing the Gr（o）bner basis of the system of Einstein equations,that＇s the generalized flag manifold M =SU（5）/U3 （1）×SU（2） admits twenty seven invariant Einstein metrics（up to a scale）,of which twelve are K（a）hler Einstein metrics and fifteen are non K（a）hler Einstein metrics.