  Elastic scattering of a wave can be quantified by a shift in the phase with
respect to the incoming wave phase. A qualitative measure of the time during
which the effect occurs is given by the Wigner time delay. The tunneling time
in turn is known to saturate with increasing tunneling barrier width (Hartman
effect). Here, we analyze the elastic quantum mechanical scattering in a
deformed one-dimensional Riemannian manifold, particularly with respect to the
Wigner time delay and conclude on the Hartman effect. It is shown that
scattering due to local curvature variations imply imperfect conduction
behavior indicating resonance states and leads to a Wigner time delay which, at
low energies, is in variance with the classical time delay that is inferred
from the arc length. At moderate and high energies, however, classical and
quantum time delays coincide.
