Tohoku Mathematical Journal
2011
March
SECOND SERIES VOL. 63, NO. 1

Tohoku Math. J.
63 (2011), 21-40

Title MOMENTUM CONSTRUCTION ON RICCI-FLAT KÄHLER CONES

Author Akito Futaki

(Received August 18, 2009)
Abstract. We extend Calabi ansatz over Kähler-Einstein manifolds to Sasaki-Einstein manifolds. As an application we prove the existence of a complete scalar-flat Kähler metric on Kähler cone manifolds over Sasaki-Einstein manifolds. n particular there exists a complete scalar-flat Kähler metric on the toric Kähler cone manifold constructed from a toric diagram with a constant height.

2000 Mathematics Subject Classification. Primary 53C55; Secondary 53C21, 55N91.
Key words and phrases. Calabi-ansatz, toric Fano manifold, Sasaki-Einstein manifold.

To the top of this page

Back to the Contents