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Gradient Ambient Obstruction Solitons on Homogeneous Manifolds

Erin Griffin

We examine homogeneous solitons of the ambient obstruction flow and, in particular, prove that any compact ambient obstruction soliton with constant scalar curvature is trivial. In doing so, we establish a number of results for solitons to the geometric flow by a general tensor $q$.
Focusing on dimension n=4, we show that any homogeneous gradient Bach soliton that is steady must be Bach flat; that the only homogeneous, non-Bach-flat, shrinking gradient solitons are product metrics on $\mathbb{R}^2×S^2$ and $\mathbb{R}^2×H^2$; and there is a homogeneous, non-Bach-flat, expanding gradient Bach soliton.