Invariant Einstein Metrics on Flag Manifolds with Four Isotropy Summands
نویسندگان
چکیده
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 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. 2000 Mathematics Subject Classification. Primary 53C25; Secondary 53C30.
منابع مشابه
Invariant Einstein Metrics on Generalized Flag Manifolds with Two Isotropy Summands
Let M = G/K be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group G. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume. 2000 Mathematics Subject Classification. Pr...
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