Momentum construction on Ricci-flat K\"ahler cones
Abstract
We extend Calabi ansatz over K\"ahler-Einstein manifolds to Sasaki-Einstein manifolds. As an application we prove the existence of a complete scalar-flat K\"ahler metric on K\"ahler cone manifolds over Sasaki-Einstein manifolds. In particular there exists a complete scalar-flat K\"ahler metric on the toric K\"ahler cone manifold constructed from a toric diagram with a constant height.
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