Invariant Einstein metrics on generalized flag manifolds with two isotropy summands

Details Invariant Einstein metrics on generalized flag manifolds with two isotropy summands Invariant Einstein metrics on generalized flag manifolds with two isotropy summands

2009-02-11

arxiv.org/abs/0902.1826v1

Mathematics

Differential Geometry

Scientific paper

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.

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