Invariant Einstein metrics on flag manifolds with four isotropy summands

Abstract

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.

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• Flag manifolds, symmetric $\fr{t}$-triples and Einstein metrics
• The classification of homogeneous Einstein metrics on flag manifolds with $b_2(M)=1$
• Invariant Generalized Complex Structures on Partial Flag Manifolds
• The projected homogeneous Ricci flow and three-isotropy-summands flag manifolds
• Homogeneous Einstein metrics on non-Kähler C-spaces