广义旗流形上不变爱因斯坦度量与结构等测地向量（英文）

Invariant Einstein metrics and structural equigeodesic vectors on genetalized flag manifolds

满旗流形SU(n)/T上至少有n!/2+n+1个不变的爱因斯坦度量,其中n!/2个是Khler爱因斯坦度量.但当n5时关于满旗流形SU(n)/T上不变爱因斯坦度量至今没有更多的结果.本文得到满旗流形SU(5)/T上在差常数倍的情况下有386个不变的爱因斯坦度量.这是用度量对满旗流形SU(n)/T(n5)进行分类的最新结果.然后作者考虑了第二Betti数为1的广义旗流形上结构等测地向量.

The full flag manifold SU（n）/Tadmits at least n!/2＋n＋1invariant Einstein metrics,of which n!/2are Khler Einstein metrics.By now,there are no more results about invariant Einstein metrics on full flag manifold SU（n）/Tfor n5.In this paper,we obtain that there are at least 386 invariant Einstein metrics（up to a scale）on the full flag manifold of SU（5）/T.This is the first known result for the classification of the full flag manifolds SU（n）/Tfor n5.Then we consider the structural equigeodesic vectors on generalized flag manifolds with b2（G/K）=1.