Invariant Einstein metrics on flag manifolds with four isotropy summands

Details Invariant Einstein metrics on flag manifolds with four isotropy summands Invariant Einstein metrics on flag manifolds with four isotropy summands

2009-04-10

arxiv.org/abs/0904.1690v2

Mathematics

Differential Geometry

Scientific paper

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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