Coupled Sasaki-Ricci solitons
Coupled Sasaki-Ricci solitons
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DOI：
10.1007/s11425-018-9499-y
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
A. Futaki;Yingying Zhang
中科院分区：
文献类型：
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作者：
A. Futaki;Yingying Zhang
受Hultgren和Witt Nyström（2018）对耦合Kähler-Einstein度规和Hultgren（2017）对耦合Kähler-Ricci孤子研究的启发，本文研究了耦合Sasaki-Einstein度规和耦合Sasaki-Ricci孤子。我们首先证明了所有横截全纯向量场的李代数和与基函数的耦合扭曲拉普拉斯算子相关的耦合基函数空间之间的同构，并得到了Kähler-Einstein度量存在的著名障碍对这种耦合情况的扩展。当Sasaki结构是正则的时，这些结果被简化为耦合的Kähler-Einstein度量。其次，我们证明了当基本的第一类陈省身是正的时，复曲面耦合的Sasaki-Einstein度量的存在性，扩展了Hultgren（2017）的工作。
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).