论文标题
缩小和扩展Ricci孤子的刚度结果
Rigidity results for shrinking and expanding Ricci solitons
论文作者
论文摘要
在本文中，我们证明了缩小和扩大Ricci孤子的刚性结果。首先，我们证明，如果我们控制电势函数的最大值，那么紧凑的收缩ricci孤子是爱因斯坦。然后，我们证明了具有捏合的Ricci和标态曲率的非紧密梯度膨胀和缩小的Ricci孤子的刚度结果，假设在无穷大的标量曲率上存在渐近条件。
In this paper, we prove some rigidity results for both shrinking and expanding Ricci solitons. First, we prove that compact shrinking Ricci solitons are Einstein if we control the maximum value of the potential function. Then, we prove some rigidity results for non-compact gradient expanding and shrinking Ricci solitons with pinched Ricci and scalar curvatures, assuming an asymptotic condition on the scalar curvature at infinity.
