Complete description of invariant Einstein metrics on the generalized flag manifold $SO(2n)/U(p)\times U(n-p)$

Abstract

We find the precise number of non-Kähler $SO(2n)$-invariant Einstein metrics on the generalized flag manifold $M=SO(2n)/U(p)\times U(n-p)$ with $n\ge 4$ and $2\le p\le n-2$. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems. We also examine the isometric problem for these Einstein metrics.

24 pages

References in corpus (1)

• Invariant Einstein metrics on flag manifolds with four isotropy summands

Cited by in corpus (3)

• Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands
• Flag manifolds, symmetric $\fr{t}$-triples and Einstein metrics
• Complex invariant Einstein metrics on $S{O}_{2(n_1+n_2+n_3)+1}/U_{n_1}\times U_{n_2}\times S{O}_{2n_3+1}$ and Ricci-flat manifolds