We study the Hull-Strominger system and the Anomaly flow on a special class of 2-step solvmanifolds, namely the class of almost-abelian Lie groups. In this setting, we characterize the existence of invariant solutions to the Hull-Strominger system with respect to the family of Gauduchon connections in the anomaly cancellation equation. Then, motivated by the results on the Anomaly flow, we investigate the flow of invariant metrics in our setting, proving that it always reduces to a flow of a special form. Finally, under an extra assumption on the initial metrics, we show that the flow is immortal and, when the slope parameter is zero, it always converges to a Kähler metric, in Cheeger-Gromov topology.

我们研究了 Hull-Strominger 系统和一类特殊的 2 步求解流形上的异常流，即几乎阿贝尔李群的类。在这种情况下，我们描述了 Hull-Strominger 系统关于异常消除方程中 Gauduchon 连接族的不变解的存在。然后，在异常流的结果的推动下，我们调查了我们设置中不变度量的流，证明它总是简化为特殊形式的流。最后，在初始度量的额外假设下，我们表明流是不朽的，并且当斜率参数为零时，它总是收敛到 Cheeger-Gromov 拓扑中的 Kähler 度量。