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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