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Invariant Einstein metrics on flag manifolds with four isotropy summands

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 0904.1690
Source
arXiv
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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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