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

Luciana Aparecida Alves; Neiton Pereira da Silva

doi:10.5269/bspm.v38i1.36604

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

Authors

Luciana Aparecida Alves Universidade Federal de Uberlândia - UFU Faculty of Mathematics
Neiton Pereira da Silva Universidade Federal de Uberlândia - UFU Faculty of Mathematics

DOI:

https://doi.org/10.5269/bspm.v38i1.36604

Keywords:

Einstein metrics, Flag manifolds, t-roots, isotropy representation

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.