New examples of Sasaki-Einstein manifolds

Abstract

In this note, stimulated by the existence result by Futaki, Ono and Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on $S^1$-bundles associated to canonical line bundles of ${\boldsymbol P}^1({\boldsymbol C})$-bundles over Kähler-Einstein Fano manifolds, even though the Futaki's obstruction does not vanish. Here our examples include non-toric Sasaki-Einstein manifolds.