  We construct effective field theories for gapped quantum Hall systems coupled
to background geometries with local Galilean invariance i.e. Bargmann
spacetimes. Along with an electromagnetic field, these backgrounds include the
effects of curved Galilean spacetimes, including torsion and a gravitational
field, allowing us to study charge, energy, stress and mass currents within a
unified framework. A shift symmetry specific to single constituent theories
constraints the effective action to couple to an effective background gauge
field and spin connection that is solved for by a self-consistent equation,
providing a manifestly covariant extension of Hoyos and Son's improvement terms
to arbitrary order in $m$.
