Momentum construction on Ricci-flat Kähler cones

Akito Futaki

doi:10.2748/tmj/1303219934

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Home > Journals > Tohoku Math. J. (2) > Volume 63 > Issue 1 > Article

2011 Momentum construction on Ricci-flat Kähler cones

Akito Futaki

Tohoku Math. J. (2) 63(1): 21-40 (2011). DOI: 10.2748/tmj/1303219934

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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. n particular there exists a complete scalar-flat Kähler metric on the toric Kähler cone manifold constructed from a toric diagram with a constant height.