论文标题
均匀歧管上的梯度环境阻塞孤子
Gradient Ambient Obstruction Solitons on Homogeneous Manifolds
论文作者
论文摘要
我们检查了环境阻塞流的同质孤子，尤其是证明具有恒定标量曲率的任何紧凑型环境阻塞是微不足道的。我们的重点是尺寸4，我们表明，任何稳定的均匀梯度Bach soliton都必须是bach平坦的，并且唯一的非BACH-FLAT缩小的梯度词素是$ \ Mathbb {r}^2 \ times s^2 $ s^2 $ and $ \ mathbb {r}^r}^r}^2^2 \ time hip time hip time h^2 $ h^2 $。我们还构建了一个非巴赫灯扩展的均匀梯度Bach Soliton。我们还通过一般张量$ q $为孤子建立了许多孤子的结果。
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. Focusing on dimension 4, we show that any homogeneous gradient Bach soliton that is steady must be Bach flat, and that the only non-Bach-flat shrinking gradient solitons are product metrics on $\mathbb{R}^2\times S^2$ and $\mathbb{R}^2 \times H^2$. We also construct a non-Bach-flat expanding homogeneous gradient Bach soliton. We also establish a number of results for solitons to the geometric flow by a general tensor $q$.
