Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

Details Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p)) Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

2010-10-21

arxiv.org/abs/1010.4472v1

Mathematics

Differential Geometry

15 pages

Scientific paper

We find the precise number of non-K\"ahler $Sp(n)$-invariant Einstein metrics
on the generalized flag manifold $M=Sp(n)/(U(p)\times U(n-p))$ with $n\geq 3$
and $1\leq p\leq n-1$. We use an analysis on parametric systems of polynomial
equations and we give some insight towards the study of such systems.

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