On non-compact gradient solitons
arXiv:2207.05822 · doi:10.1007/s11005-022-01582-7
Abstract
In this paper we extend existing results for generalized solitons, called -solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field and curvature conditions on , we are able to use the chosen properties of the tensor to see that such non-compact -solitons are stationary and -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.
Necessary update after major changes to theorem numbering and corrections were made