Momentum construction on Ricci-flat Kähler cones

Details Momentum construction on Ricci-flat Kähler cones Momentum construction on Ricci-flat Kähler cones

2007-03-05

arxiv.org/abs/math/0703138v2

Tohoku Math.J.63:21-40,2011

Mathematics

Differential Geometry

18 pages. The title is changed. Statements with incomplete proofs are modified

Scientific paper

10.2748/tmj/1303219934

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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