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

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

2010-06-28

arxiv.org/abs/1006.5294v1

Mathematics

Differential Geometry

24 pages

Scientific paper

We find the precise number of non-K\"ahler $SO(2n)$-invariant Einstein
metrics on the generalized flag manifold $M=SO(2n)/U(p)\times U(n-p)$ with
$n\geq 4$ and $2\leq p\leq n-2$. 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.

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