Momentum construction on Ricci-flat Kähler cones
arXiv:math/0703138 · doi:10.2748/tmj/1303219934
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. In particular there exists a complete scalar-flat Kähler metric on the toric Kähler cone manifold constructed from a toric diagram with a constant height.
18 pages. The title is changed. Statements with incomplete proofs are modified