论文标题
在非紧密梯度孤子上
On non-compact gradient solitons
论文作者
论文摘要
在本文中，我们通过考虑非紧凑型孤子来将通用孤子的现有结果（称为$ q $ -solitons）扩展到完整的情况下。通过将规律性条件放在向量字段$ x $和在$ m $上的曲率条件上，我们可以使用张量$ q $的选定属性，以查看这种非紧凑型$ q $ -solitons是固定的和$ q $ -flat。 最后，我们将结果应用于环境阻塞孤子，棉孤子和巴赫孤子的示例，以证明这些一般定理对各种流的实用性。
In this paper we extend existing results for generalized solitons, called $q$-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field $X$ and curvature conditions on $M$, we are able to use the chosen properties of the tensor $q$ to see that such non-compact $q$-solitons are stationary and $q$-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.
