关于非紧化梯度孤子

Pub Date : 2023-05-24 DOI:10.1007/s10455-023-09904-1

Antonio W. Cunha, Erin Griffin

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引用次数: 1

摘要

在本文中，我们通过考虑非紧孤子，将广义孤子（称为q孤子）的现有结果推广到完全情况。通过在向量场X上设置正则性条件，在M上设置曲率条件，我们能够使用张量q的所选性质来看到这种非紧q孤子是静止的且q平坦的。最后，我们将我们的结果应用于环境阻塞孤子、Cotton孤子和Bach孤子的例子，以证明这些一般定理对各种流动的效用。

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On non-compact gradient solitons

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.

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