Constructing Kähler-Ricci Solitons from Sasaki-Einstein Manifolds

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.

Keywords

Ricci soliton, Sasaki-Einstein manifold, toric Fano manifold

2010 Mathematics Subject Classification

Primary 53C55. Secondary 53C21, 55N91.

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Published 30 March 2011