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Transactions of the American Mathematical Society

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New invariant Einstein metrics on generalized flag manifolds

Author: Andreas Arvanitoyeorgos
Journal: Trans. Amer. Math. Soc. 337 (1993), 981-995
MSC: Primary 53C25; Secondary 53C30
MathSciNet review: 1097162
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Abstract: A generalized flag manifold (or a Kählerian $ C$-space) is a homogeneous space $ G/K$ whose isotropy subgroup $ K$ is the centralizer of a torus in $ G$. These spaces admit a finite number of Kähler-Einstein metrics. We present new non-Kahler Einstein metrics for certain quotients of $ U(n)$, $ SO(2n)$ and $ {G_2}$. We also examine the isometry question for these metrics.

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