  Conformal geometry is considered within a general relativistic framework. An
invariant distant for proper time is defined and a parallel displacement is
applied in the distorted space-time, modifying Einstein's equation
appropriately. A particular solution is introduced for the covariant
acceleration potential that matches the observed velocity distribution at large
distances from the galactic centre, i.e. Modified Newtonian Dynamics (MOND).
This explicit solution, of a general framework that allows both curvature and
explicit local expansion of space-time, thus reproduces the observed flattening
of galaxys' rotation curves without the need to assume the existence of dark
matter. The large distance expansion rate is found to match the speed of a
spherical shock wave.
