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

2014/11/12 by Luciana Aparecida Alves, Alves, Luciana Aparecida, Neiton Pereira da Silva +1 · 1 citation
Mathematics · #53C25 53C30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1411.3170

27 pages

arxiv created 2014/11/12 · arxiv updated 2014/11/13

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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