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

Andreas Arvanitoyeorgos; Ioannis Chrysikos; Yusuke Sakane

paper

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

arXiv:1010.4472

Abstract

We find the precise number of non-Kähler $S p (n)$ -invariant Einstein metrics on the generalized flag manifold $M = S p (n) / (U (p) \times U (n - p))$ 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.

arXiv comment15 pages