Gradient ambient obstruction solitons on homogeneous manifolds

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