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.

中文翻译：

---

关于非紧梯度孤子

在本文中，我们通过考虑非紧凑孤子，将广义孤子（称为q孤子）的现有结果扩展到完整情况。通过在矢量场X上设置正则性条件并在M上设置曲率条件，我们能够使用张量q的选定属性来查看此类非紧凑q -孤子是平稳的且q -平坦的。最后，我们将我们的结果应用于环境障碍孤子、棉花孤子和巴赫孤子的例子，以证明这些一般定理对各种流的效用。