  We propose homogeneous metrics of Petrov type III that describe gyrating
Schrodinger geometries as duals to some non-relativistic field theories, in
which the Schrodinger symmetry is broken further so that the phase space has a
linear dependence of the momentum in a selected direction. We show that such
solutions can arise in four-dimensional Einstein-Weyl supergravity as well as
higher-dimensional extended gravities with quadratic curvature terms coupled to
a massive vector. In Einstein-Weyl supergravity, the gyrating Schrodinger
solutions can be supersymmetric, preserving 1/4 of the supersymmetry. We obtain
the exact Green function in the phase space associated with a bulk free massive
scalar.
