``Hall viscosity'', edge-state dipole moments and incompressibility of FQHE fluids

The dissipationless ``Hall viscosity'' described for the inte- ger QHE by Avron \textit{et al.} (1995) and for the FQHE by Read (2009) describes the stress-tensor response to the gradient of the electric field, and is distinct from the Hall conductivity. Previous work assumed rotational invariance and an extrinsic metric; removing this unnecessary assumption (broken by ``tilting'' B) clarifies the relations between Hall viscosity and incompressibility. New properties of FQHE fluids emerge:(1) they have no hydrostatic pressure; (2) (unreconstructed) edges have a universal electric dipole moment given by the Hall viscosity, which (3) has \textit{two} distinct sources, the ``smearing'' of electron density relative to guiding center density and non-trivial behavior of guiding-center occupations near an edge. (4) The second term vanishes in the integer QHE, is odd under particle-hole symmetry, and is expressed in terms of a modified ``shift'' (per flux, as opposed to per particle, as in Read 2009), plus (5) an intrinsic metric that arises from incompressibility itself. (6) Its absolute value provides a lower bound to the coefficient of $Q^4$ behavior of the the guiding-center structure function as $Q \rightarrow 0$, (and is an equality for model states such as Laughlin, Moore-Read.) These properties are related through the $SO$(2,1) algebra of guiding-center deformations.