Coupled Sasaki-Ricci solitons

Akito Futaki Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Yingying Zhang Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Differential Geometry mathscidoc:2204.10003

Science China Mathematics, 64, (7), 1447-1462, 2019.6
Motivated by the study of coupled Kähler-Einstein metrics by Hultgren and Witt Nyström (2018) and coupled Kähler-Ricci solitons by Hultgren (2017), we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki-Ricci solitons. We first show an isomorphism between the Lie algebra of all transverse holomorphic vector fields and certain space of coupled basic functions related to coupled twisted Laplacians for basic functions, and obtain extensions of the well-known obstructions to the existence of Kähler-Einstein metrics to this coupled case. These results are reduced to coupled Kähler-Einstein metrics when the Sasaki structure is regular. Secondly we show the existence of toric coupled Sasaki-Einstein metrics when the basic first Chern class is positive extending the work of Hultgren (2017).
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  title={Coupled Sasaki-Ricci solitons},
  author={Akito Futaki, and Yingying Zhang},
  booktitle={Science China Mathematics},
Akito Futaki, and Yingying Zhang. Coupled Sasaki-Ricci solitons. 2019. Vol. 64. In Science China Mathematics. pp.1447-1462.
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