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Momentum construction on Ricci-flat Kähler cones

Akito Futaki
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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.

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Akito Futaki. 2009-07-27. Momentum construction on Ricci-flat Kähler cones. https://doi.org/10.2748/tmj%2F1303219934

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