  For the Riemannian space, built from the collective coordinates used within
nuclear models, an additional interaction with the metric is investigated,
using the collective equivalent to Einstein's curvature scalar. The coupling
strength is determined using a fit with the AME2003 ground state masses. An
extended finite-range droplet model including curvature is introduced, which
generates significant improvements for light nuclei and nuclei in the
trans-fermium region.
