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arXiv · 2207.05822

On non-compact gradient solitons

Antonio W. Cunha·Erin Griffin
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Abstract

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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BibTeXRIS

Antonio W. Cunha, Erin Griffin. 2022-07-12. On non-compact gradient solitons. https://doi.org/10.1007/s11005-022-01582-7

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