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 Strominger-Bismut connection.

我们研究了关于 Gauduchon 线中任何 Hermitian 连接的 2 步 nilmanifolds 上的异常流。在平坦的全纯丛的情况下，对于任何初始不变的 Hermitian 度量给出了异常流的一般解。解取决于两个常数\(K_1\)和\(K_2\)，我们研究了异常流的定性行为，它们的符号以及 Gromov-Hausdorff 拓扑中的收敛性。\(K_1\)的符号与 Fu、Wang 和 Wu 引入的保形不变量有关。在非平坦情况下，我们找到了在某些初始假设下异常流的一般演化方程。这使我们能够在具体的 nilmanifold 上检测 Hull-Strominger-Ivanov 系统的非平坦解，这些解相对于 Strominger-Bismut 连接表现为异常流的驻点。