  We apply differential geometry methods to the computation of the
anomaly-induced hydrodynamic equilibrium partition function. Implementing the
imaginary-time prescription on the Chern-Simons effective action on a
stationary background, we obtain general closed expressions for both the
invariant and anomalous part of the partition function. This is applied to the
Wess-Zumino-Witten action for Goldstone modes, giving the equilibrium partition
function of superfluids. In all cases, we also study the anomaly-induced gauge
currents and energy-momentum tensor, providing explicit expressions for them.
