  We study off-shell rigid limits for the kinetic and scalar-potential terms os
a single N=2 hypermultiplet. In the kinetic term, these rigid limits establish
relations between four-dimensional quaternion-Kahler and hyper-Kahler target
spaces with symmetry. The scalar potential is obtained by gauging the
graviphoton along an isometry of the quaternion-Kahler space. The rigid limits
unveil two distinct cases. A rigid N=2 theory on Minkowski or on AdS_4
spacetime, depending on whether the isometry is translational or rotational
respectively. We apply these results to the quaternion-Kahler space with
Heisenberg x U(1) isometry, which describes the universal hypermultiplet at
type-II string one-loop.
