论文标题
在Fano Kaehler-Irci Solitons的空间上的Weil-Petersson型公制
A Weil-Petersson Type Metric on the Space of Fano Kaehler-Ricci Solitons
论文作者
论文摘要
在本文中，我们在缩小Kaehler-Icci solitons的空间中定义了一个Weil-Petersson型度量，并在与Kaehler-Ricci Soliton指标的选择无关时，证明了它是必要且充分的条件。我们还表明，Weil-Petersson指标是Kaehler，当它在Kuranishi空间上定义了Fano Kaehler-Irci Solitons的小变形空间时。最后，我们建立了FanoKähler-Icci solitons的第一阶和二阶变形，并表明，从本质上讲，在变形Kaehler-Icci Solitons中，第一个有效术语导致Weil-Petersson指标。
In this paper we define a Weil-Petersson type metric on the space of shrinking Kaehler-Ricci solitons and prove a necessary and sufficient condition on when it is independent of the choices of Kaehler-Ricci soliton metrics. We also show that the Weil-Petersson metric is Kaehler when it defines a metric on the Kuranishi space of small deformations of Fano Kaehler-Ricci solitons. Finally, we establish the first and second order deformation of Fano Kähler-Ricci solitons and show that, essentially, the first effective term in deforming Kaehler-Ricci solitons leads to the Weil-Petersson metric.
