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

Luciana Aparecida Alves; Neiton Pereira da Silva

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

Differential Geometry 2014-11-13 v1

Authors: Luciana Aparecida Alves , Neiton Pereira da Silva

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 $D_n$ .

Keywords

Einstein equation flag manifolds invariant metrics isotropy summands classical Lie groups t-roots algebraic system

Cite

@article{arxiv.1411.3170,
  title  = {Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds},
  author = {Luciana Aparecida Alves and Neiton Pereira da Silva},
  journal= {arXiv preprint arXiv:1411.3170},
  year   = {2014}
}

Comments

27 pages

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