In this talk I will discuss how differential geometry methods can be applied to the computation of the equilibrium partition function of anomalous fluids, as well as their associated currents. In the case of systems with spontaneous symmetry breaking, a direct calculation of the covariant currents is possible without relying on a previous evaluation of the, usually cumbersome, WZW effective action of Goldstone bosons. As an example, I will present the computation of the anomalous transport coefficients of a two-flavor chiral hadronic superfluid.