%0 Journal Article
%T Invariant Einstein metrics on flag manifolds with four isotropy summands
%A Andreas Arvanitoyeorgos
%A Ioannis Chrysikos
%J Mathematics
%D 2009
%I arXiv
%X A generalized flag manifold is a homogeneous space of the form $G/K$, where $K$ is the centralizer of a torus in a compact connected semisimple Lie group $G$. We classify all flag manifolds with four isotropy summands and we study their geometry. We present new $G$-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics.
%U http://arxiv.org/abs/0904.1690v2