Motivated by the study of coupled Kahler-Einstein metrics by Hultgren and Witt Nystrom(2018)and coupled Kahler-Ricci solitons by Hultgren(2017),we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki...Motivated by the study of coupled Kahler-Einstein metrics by Hultgren and Witt Nystrom(2018)and coupled Kahler-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 Kahler-Einstein metrics to this coupled case.These results are reduced to coupled Kahler-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).展开更多
文摘Motivated by the study of coupled Kahler-Einstein metrics by Hultgren and Witt Nystrom(2018)and coupled Kahler-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 Kahler-Einstein metrics to this coupled case.These results are reduced to coupled Kahler-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).
