  Exploiting novel aspects of the quantum geometry of charged particles in a
magnetic field via gauge-invariant variables, we provide tangible connections
between the response of quantum Hall fluids to non-uniform electric fields and
the characteristic geometry of electronic motion in the presence of magnetic
and electric fields. The geometric picture we provide motivates the following
conjecture: non-uniform electric fields mimic the presence of spatial
curvature. Consequently, the gravitational coupling constant also appears in
the charge response to non-uniform electric fields.
