论文标题
四维完整梯度收缩Ricci孤子
Four-dimensional complete gradient shrinking Ricci solitons
论文作者
论文摘要
在本文中，我们研究了四维完整的梯度收缩Ricci孤子。我们证明，涉及Weyl Tensor的自动划分或反自我偶的部分的四维完整梯度收缩Ricci soliton满足了尖锐的条件，weyl Tensor是Einstein，或者是爱因斯坦，或者是高斯缩水solinking solinking solinking solinking solinking solink $ \ bbb {r}^4，$}^4，$}^4，$}^4，$} $ \ bbb {s}^{3} \ times \ bbb {r} $，或$ \ bbb {s}^{2}^{2} \ times \ bbb {r}^{2} $。此外，我们提供了一定范围的整个阶级稳定性，该级别均可通过稳定范围来确定其范围的范围。
In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton $\Bbb{R}^4,$ or $\Bbb{S}^{3}\times\Bbb{R}$, or $\Bbb{S}^{2}\times\Bbb{R}^{2}.$ In addition, we provide some curvature estimates for four-dimensional complete gradient Ricci solitons assuming that its scalar curvature is suitable bounded by the potential function.
