Constructing Kahler-Ricci solitons from Sasaki-Einstein manifolds

Akito Futaki The University of Tokyo Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10044

Asian Journal of Mathematics , 15, (1), 33-52, 2011
We construct gradient K\"ahler-Ricci solitons on Ricci-flat K\"ahler 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.
Ricci soliton, Sasaki-Einstein manifold, toric Fano manifold.
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  title={Constructing Kahler-Ricci solitons from Sasaki-Einstein manifolds},
  author={Akito Futaki, and Mu-Tao Wang},
  booktitle={Asian Journal of Mathematics },
Akito Futaki, and Mu-Tao Wang. Constructing Kahler-Ricci solitons from Sasaki-Einstein manifolds. 2011. Vol. 15. In Asian Journal of Mathematics . pp.33-52.
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