论文标题
简单连接的Nilmanifolds的BACH流
Bach Flow of Simply Connected Nilmanifolds
论文作者
论文摘要
BACH流是在四个歧管上定义的第四阶几何流程。对于紧凑的歧管，它是Weyl曲率的$ l^2 $ norm的形式修改的梯度流。在本文中，我们研究了四维的BACH流，简单地连接的nilmanifolds，其谎言代数是不可分解的。我们表明，从任意左左不变度开始的BACH流量存在于所有积极的时间，并且在尖锐的Cheeger-Gromov Sense重新分组后，趋向于扩展的Bach Soliton，这是非毕业者的。将我们的结果与Helliwell的先前结果相结合，对简单连接的Nilmanifolds上的Bach流进行了完整的描述。
The Bach flow is a fourth order geometric flow defined on four manifolds. For a compact manifold, it is a conformally modified gradient flow for the $L^2$-norm of the Weyl curvature. In this paper we study the Bach flow on four-dimensional simply connected nilmanifolds whose Lie algebra is indecomposable. We show that the Bach flow beginning at an arbitrary left invariant metric exists for all positive times and after rescaling converges in the pointed Cheeger-Gromov sense to an expanding Bach soliton which is non-gradient. Combining our results with previous results of Helliwell gives a complete description of the Bach flow on simply connected nilmanifolds.
