Momentum construction on Ricci-flat K'ahler cones

摘要

We extend Calabi ansatz over K\"ahler-Einstein manifolds to Sasaki-Einsteinmanifolds. As an application we prove the existence of a complete scalar-flatK\"ahler metric on K\"ahler cone manifolds over Sasaki-Einstein manifolds. Inparticular there exists a complete scalar-flat K\"ahler metric on the toricK\"ahler cone manifold constructed from a toric diagram with a constant height.