Tohoku Mathematical Journal

Momentum construction on Ricci-flat Kähler cones

Akito Futaki

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 63, Number 1 (2011), 21-40.

Dates
First available in Project Euclid: 19 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1303219934

Digital Object Identifier
doi:10.2748/tmj/1303219934

Mathematical Reviews number (MathSciNet)
MR2788774

Zentralblatt MATH identifier
1227.53084

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 55N91: Equivariant homology and cohomology [See also 19L47]

Keywords
Calabi-ansatz toric Fano manifold Sasaki-Einstein manifold

Citation

Futaki, Akito. Momentum construction on Ricci-flat Kähler cones. Tohoku Math. J. (2) 63 (2011), no. 1, 21--40. doi:10.2748/tmj/1303219934. https://projecteuclid.org/euclid.tmj/1303219934


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