  We construct curved backgrounds with Euclidean signature admitting rigid
supersymmetry by using a 5d N=1 off-shell Poincare supergravity. We solve the
conditions for the background Weyl multiplet and vector multiplets that
preserve at least one supersymmetry parameterized by a symplectic Majorana
spinor, and represent the solution in terms of several independent fields. We
also show that the partition function does not depends on the local degrees of
freedom of the background fields. Namely, as far as we focus on a single
coordinate patch, we can freely change the independent fields by combining
Q-exact deformations and gauge transformations. We also discuss realization of
several known examples of supersymmetric theories in curved backgrounds by
using the supergravity.
