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arXiv · 1411.3170

Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds

Luciana Aparecida Alves·Neiton Pereira da Silva
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Abstract

It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to a algebraic system, if $g$ is a $G$-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We also determined the number of isotropy summands for all of these spaces and proved certain properties of the set of t-roots for flag manifolds of type $B_n$, $C_n$ and $D_n$.

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Luciana Aparecida Alves, Neiton Pereira da Silva. 2014-11-12. Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds. https://arxiv.org/abs/1411.3170

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