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 $SO(2n)$

Autores

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

Palavras-chave:

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

Resumo

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.

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Publicado

2018-02-19

Edição

v. 38 n. 1 (2020)

Seção

Artigos

Licença

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

Como Citar

Alves, L. A., & Silva, N. P. da. (2018). Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$. Boletim Da Sociedade Paranaense De Matemática, 38(1), 227-242. https://doi.org/10.5269/bspm.v38i1.36604