  The Bach equation and the equation of geometrodynamics are based on two quite
different physical motivations, but in both approaches, the conformal
properties of gravitation plays the key role. In this paper we present an
analysis of the relation between these two equations and show that the
solutions of the equation of geometrodynamics are of a more general nature. We
show the following non-trivial result: there exists a conformally invariant
Lagrangian, whose field equation generalizes the Bach equation and has as
solutions those Ricci tensors which are solutions to the equation of
geometrodynamics.
