Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous Einstein metrics on generalized flag manifolds with five
  isotropy summands   We construct the homogeneous Einstein equation for generalized flag manifolds
$G/K$ of a compact simple Lie group $G$ whose isotropy representation
decomposes into five inequivalent irreducible $\Ad(K)$-submodules. To this end
we apply a new technique which is based on a fibration of a flag manifold over
another flag manifold and the theory of Riemannian submersions. We classify all
generalized flag manifolds with five isotropy summands, and we use Gr\"obner
bases to study the corresponding polynomial systems for the Einstein equation.
For the generalized flag manifolds E_6/(SU(4) x SU(2) x U (1) x U (1)) and
E_7/(U(1) x U(6)) we find explicitely all invariant Einstein metrics up to
isometry. For the generalized flag manifolds SO(2\ell +1)/(U(1) x U (p) x
SO(2(\ell -p-1)+1)) and SO(2\ell)/(U(1) x U (p) x SO(2(\ell -p-1))) we prove
existence of at least two non K\"ahler-Einstein metrics. For small values of
$\ell$ and $p$ we give the precise number of invariant Einstein metrics.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex