  The notion of uniform and/or constant tensor fields of rank $>0$ is
incompatible with general curved spacetimes. This work considers the
consequences of certain tensor-valued coefficients for Lorentz violation in the
Standard-Model Extension varying with spacetime position. We focus on two of
the coefficients, $a_\mu$ and $b_\mu$, that characterize Lorentz violation in
massive fermions, particularly in those fermions that constitute ordinary
matter. We calculate the nonrelativistic hamiltonian describing these effects,
and use it to extract the sensitivity of several precision experiments to
coefficient variation.
