  This paper considers 4-dimensional manifolds upon which there is a Lorentz
metric, h, and a symmetric connection and which are originally assumed
unrelated. It then derives sufficient conditions on the metric and connection
(expressed through the curvature tensor) for the connection to be the
Levi-Civita connection of some (local) Lorentz metric, g, and calculates the
relationship between g and h. Some examples are provided which help to assess
the strength of the sufficient conditions derived.
