  Two ultra diffuse galaxies in the same group, NGC1052-DF2 and NGC1052-DF4,
have been found to have little or no dark matter and to host unusually luminous
globular cluster populations. Such low mass diffuse objects in a group
environment are easily disrupted and are expected to show evidence of tidal
distortions. In this work we present deep new imaging of the NGC1052 group,
obtained with the Dragonfly Telephoto Array, to test this hypothesis. We find
that both galaxies show strong position angle twists and are significantly more
elongated at their outskirts than in their interiors. The group's central
massive elliptical NGC1052 is the most likely source of these tidal
disturbances. The observed distortions imply that the galaxies have a low total
mass or are very close to NGC1052. Considering constraints on the galaxies'
relative distances, we infer that the dark matter halo masses of these galaxies
cannot be much greater than their stellar masses. Calculating pericenters from
the distortions, we find that the galaxies are on highly elliptical orbits,
with a ratio of pericenter to present-day radius Rperi/R0~0.1 if the galaxies
are dark matter-free and Rperi/R0~0.01 if they have a normal dark halo. Our
findings provide strong evidence, independent of kinematic constraints, that
both galaxies are dark matter deficient. Furthermore, the similarity of the
tidal features in NGC1052-DF2 and NGC1052-DF4 strongly suggests that they arose
at comparable distances from NGC1052. In Appendix A, we describe sbcontrast, a
robust method to determine the surface brightness limit of images.
