Abstract
We examine the space of solutions to the affine quasi–Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitons, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. We use the dimension of the space of affine Killing vector fields to structure our discussion as this provides a convenient organizational framework.
Communicated by: P. Eberlein
Funding: Supported by projects MTM2016-75897-P and ED431C 2019/10 with FEDER Funds (Spain).
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