Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Luciana Aparecida Alves; Neiton Pereira da Silva

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

Differential Geometry 2016-06-09 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 an algebraic system if $g$ is a $G$ -invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$ ; and we compute the Einstein system for generalized flag manifolds of type $Sp(n)$ . We also consider the isometric problem for these Einstein metrics.

Keywords

invariant Einstein metrics generalized flag manifolds Riemannian flag manifold Einstein equation isometric problem

Cite

@article{arxiv.1606.02539,
  title  = {Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$},
  author = {Luciana Aparecida Alves and Neiton Pereira da Silva},
  journal= {arXiv preprint arXiv:1606.02539},
  year   = {2016}
}

Comments

The article has 13 pages and 1 table. arXiv admin note: substantial text overlap with arXiv:1411.3170

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