Asian Journal of Mathematics

Constructing Kähler-Ricci Solitons from Sasaki-Einstein Manifolds

Akito Futaki and Mu-Tao Wang

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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

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

First available in Project Euclid: 28 May 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Ricci soliton Sasaki-Einstein manifold toric Fano manifold


Futaki, Akito; Wang, Mu-Tao. Constructing Kähler-Ricci Solitons from Sasaki-Einstein Manifolds. Asian J. Math. 15 (2011), no. 1, 33--52.

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