New invariant Einstein metrics on generalized flag manifolds

Andreas Arvanitoyeorgos
1993 Transactions of the American Mathematical Society  
A generalized flag manifold (or a Kählerian C-space) is a homogeneous space G/K whose isotropy subgroup K is the centralizer of a torus in G . These spaces admit a finite number of Kähler-Einstein metrics. We present new non-Kähler Einstein metrics for certain quotients of [/(«), SO(2n) and (?2 . We also examine the isometry question for these metrics.
doi:10.1090/s0002-9947-1993-1097162-3 fatcat:a3jxgh242jfbhoo3chjh2zn54e