论文标题
Nilmanifolds的异常流
The Anomaly flow on nilmanifolds
论文作者
论文摘要
我们研究了Gauduchon系列中任何遗产连接的$ 2 $步骤Nilmanifolds的异常流。在平坦的全体形态束的情况下，对于任何初始不变的Hermitian度量，给出了异常流的一般解决方案。该解决方案取决于两个常数$ k_1 $和$ k_2 $，我们从其迹象方面研究异常流的定性行为以及Gromov-Hausdorff拓扑的融合。 $ k_1 $的标志与Fu，Wang和Wu引入的保形不变有关。在非平局情况下，我们在某些初始假设下发现异常流的一般演化方程。这使我们能够检测到混凝土尼尔曼福尔德（Nilmanifold）上赫尔 - 斯托林格 - 凡诺夫系统（Hull-Strominger-Ivanov）系统的非燃料溶液，该溶液与bismut连接相对于异常流的固定点。
We study the Anomaly flow on $2$-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants $K_1$ and $K_2$, and we study the qualitative behaviour of the Anomaly flow in terms of their signs, as well as the convergence in Gromov-Hausdorff topology. The sign of $K_1$ is related to the conformal invariant introduced by Fu, Wang and Wu. In the non-flat case, we find the general evolution equations of the Anomaly flow under certain initial assumptions. This allows us to detect non-flat solutions to the Hull-Strominger-Ivanov system on a concrete nilmanifold, which appear as stationary points of the Anomaly flow with respect to the Bismut connection.
