Constructing Kähler-Ricci solitons from Sasaki-Einstein manifolds

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.

Final version, to appear in Asian J. Math

References in corpus (3)

• Gaussian densities and stability for some Ricci solitons
• A characterization of Koiso's typed solitons
• Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows

Cited by in corpus (3)

• Classification results for expanding and shrinking gradient Kähler-Ricci solitons
• Rotational Symmetry of Conical Kähler-Ricci Solitons
• Constructing soliton solutions of geometric flows by separation of variables