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 by the use of \({\mathfrak{t}}\)-roots. 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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Arvanitoyeorgos, A., Chrysikos, I. Invariant Einstein metrics on flag manifolds with four isotropy summands. Ann Glob Anal Geom 37, 185–219 (2010). https://doi.org/10.1007/s10455-009-9183-7
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DOI: https://doi.org/10.1007/s10455-009-9183-7
Keywords
- Homogeneous manifold
- Einstein metric
- Generalized flag manifold
- Isotropy representation
- \({\mathfrak{t}}\)-roots