Momentum construction on Ricci-flat K?hler cones

摘要

We extend Calabi ansatz over K?hler-Einstein manifolds to Sasaki-Einstein manifolds. As an application we prove the existence of a complete scalar-flat K?hler metric on K?hler cone manifolds over Sasaki-Einstein manifolds. n particular there exists a complete scalar-flat K?hler metric on the toric K?hler cone manifold constructed from a toric diagram with a constant height.