We prove that there is exactly one homothety class of invariant Einstein metrics in each space $SU(2) \times SU(2) / SO(2)_r (r\in Q, \, |r|\neq 1)$ defined below.
@article{116981,
author = {Eugene D. Rodionov},
title = {Einstein metrics on a class of five-dimensional homogeneous spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {32},
year = {1991},
pages = {389-393},
zbl = {0747.53037},
mrnumber = {1137801},
language = {en},
url = {http://dml.mathdoc.fr/item/116981}
}
Rodionov, Eugene D. Einstein metrics on a class of five-dimensional homogeneous spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 389-393. http://gdmltest.u-ga.fr/item/116981/
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