论文标题
$ s^1 $ -INVARIANT LAPLACIAN流
$S^1$-invariant Laplacian flow
论文作者
论文摘要
Laplacian流是科比引入的几何流程，是寻找无扭转$ g_2 $结构的一种方式。如果流量为$ s^1 $ invariant，则它将下降到$ su（3）$ - $ 6 $ manifold上的流程。在本文中，我们得出了这些进化方程的表达式。在搜索示例时，我们发现了第一个不均匀的萎缩孤子，这也是梯度。我们还表明，任何紧凑的无扭力孤子都不容纳无限的对称性。
The Laplacian flow is a geometric flow introduced by Bryant as a way for finding torsion free $G_2$-structures. If the flow is $S^1$-invariant then it descends to a flow of $SU(3)$-structures on a $6$-manifold. In this article we derive expressions for these evolution equations. In our search for examples we discover the first inhomogeneous shrinking solitons, which are also gradient. We also show that any compact non-torsion free soliton admits no infinitesimal symmetry.
