The anomaly flow on nilmanifolds

We study the Anomaly flow on $2$-step nilmanifolds with respect to any Hermitian connection in Gauduchon line. In case of flat holomorphic bundle, general solution is given for initial invariant metric. The solutions depend two constants $K_1$ and $K_2$, we qualitative behaviour terms their signs, as well convergence Gromov-Hausdorff topology. sign related conformal introduced by Fu, Wang Wu. non-flat case, find evolution equations under certain assumptions. This allows us detect Hull-Strominger-Ivanov system a concrete nilmanifold, which appear stationary points Bismut connection.