Tohoku Mathematical Journal
2013
June
SECOND SERIES VOL. 65, NO. 2

Tohoku Math. J.
65 (2013), 243-252

Title NEW EXAMPLES OF SASAKI-EINSTEIN MANIFOLDS

Dedicated to the memory of Professor Shoshichi Kobayashi
Author Toshiki Mabuchi and Yasuhiro Nakagawa

(Received April 5, 2011, revised July 25, 2012)
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.

Mathematics Subject Classification. Primary 53C25; Secondary 32Q20, 53C55.
Key words and phrases. Sasaki manifolds, Sasaki-Einstein metrics, the Reeb field, Kähler-Ricci solitons, transverse holomorphic structures, Koiso-Sakane's examples, non-toric Sasaki-Einstein manifolds.

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