论文标题
四维kähler-icci solitons的刚度
Rigidity of four-dimensional Kähler-Ricci solitons
论文作者
论文摘要
在本文中，我们研究了接近Kähler模型的四维梯度收缩Ricci Soliton。第一个定理可以将其视为$ \ mathbb {s}^2 \ times \ times \ mathbb {r}^2 $（从备注1）上的kähler-ricci soliton结构的刚度结果。此外，我们表明，如果在特定意义上，自偶联的Weyl张量和标量曲率的标准与Kähler指标上的标准曲率接近，那么梯度Ricci Soliton必须是半吻合平坦的或本地的Kähler。
In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a Kähler model. The first theorem could be considered as a rigidity result for the Kähler-Ricci soliton structure on $\mathbb{S}^2\times \mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a Kähler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally Kähler.
