论文标题
Sasaki歧管上的瞬间多面体和体积最小化
Moment polytopes on Sasaki manifolds and volume minimization
论文作者
论文摘要
我们表明，横向耦合的Kähler-Einstein指标在曲奇sasaki歧管上作为体积功能的临界点出现。作为证明的准备，我们在Reeb矢量场的变化下重新介绍了横向矩多形和接触力矩多形。然后，我们将其应用于Martelli-Sparks-Yau的量最小化的耦合版本。 This is done assuming the Calabi-Yau condition of the Kähler cone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.
We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kähler cone, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.
