Asian Journal of Mathematics

Constructing Kähler-Ricci Solitons from Sasaki-Einstein Manifolds

Akito Futaki and Mu-Tao Wang

Full-text: Open access

Abstract

We construct gradient Kähler-Ricci solitons on Ricci-flat Kähler cone manifolds and on line bundles over toric Fano manifolds. Certain shrinking and expanding solitons are pasted together to form eternal solutions of the Ricci flow. The method we employ is the Calabi ansatz over Sasaki-Einstein manifolds, and the results generalize constructions of Cao and Feldman-Ilmanen- Knopf.

Article information

Source
Asian J. Math., Volume 15, Number 1 (2011), 33-52.

Dates
First available in Project Euclid: 28 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1306616063

Mathematical Reviews number (MathSciNet)
MR2786464

Zentralblatt MATH identifier
1222.53074

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
Ricci soliton Sasaki-Einstein manifold toric Fano manifold

Citation

Futaki, Akito; Wang, Mu-Tao. Constructing Kähler-Ricci Solitons from Sasaki-Einstein Manifolds. Asian J. Math. 15 (2011), no. 1, 33--52. https://projecteuclid.org/euclid.ajm/1306616063


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