Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries

We prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on $\mathbb{R}^3$ that are invariant under the natural cohomogeneity one action of SO(3). In the context of generalized Ricci flow, this result represents the analogue of Bryant's construction of the complete rotationally invariant steady soliton for the Ricci flow.