We show that there exists exactly one homothety class of invariant Einstein metrics on each space $[SU(2)]^{S+1}/T^S$ defined below.
@article{107451,
author = {Eugene D. Rodionov},
title = {On a new family of homogeneous Einstein manifolds},
journal = {Archivum Mathematicum},
volume = {028},
year = {1992},
pages = {199-204},
zbl = {0787.53037},
mrnumber = {1222287},
language = {en},
url = {http://dml.mathdoc.fr/item/107451}
}
Rodionov, Eugene D. On a new family of homogeneous Einstein manifolds. Archivum Mathematicum, Tome 028 (1992) pp. 199-204. http://gdmltest.u-ga.fr/item/107451/
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