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## Gradient Ambient Obstruction Solitons on Homogeneous Manifolds

### Erin Griffin

#### Seattle Pacific University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloaka4e01d9e7bd5b2902e0ab382a0f497b0').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addya4e01d9e7bd5b2902e0ab382a0f497b0 = '&#101;r&#105;ngr&#105;ff&#105;n003' + '&#64;'; addya4e01d9e7bd5b2902e0ab382a0f497b0 = addya4e01d9e7bd5b2902e0ab382a0f497b0 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_texta4e01d9e7bd5b2902e0ab382a0f497b0 = '&#101;r&#105;ngr&#105;ff&#105;n003' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloaka4e01d9e7bd5b2902e0ab382a0f497b0').innerHTML += '<a ' + path + '\'' + prefix + ':' + addya4e01d9e7bd5b2902e0ab382a0f497b0 + '\'>'+addy_texta4e01d9e7bd5b2902e0ab382a0f497b0+'<\/a>';

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.