  Adiabatic transport in a many-electron system is expressed in terms of the
appropriate Berry curvature, owing to the Niu-Thouless theory [J. Phys A {\bf
17}, 2453 (1984)]; the main equation is very compact and very general. I
address here three paradigmatic adiabatic response tensors -- -the atomic polar
tensor, the atomic axial tensor, and the rotational $g$ factor -- and I show
that, for all of them, the known formulas do not need an independent proof.
They are just case studies of the general expression, for different choices the
curvature's two arguments.
