  We determine, in the context of five-dimensional ${\cal N}=2$ gauged
supergravity with vector and hypermultiplets, the conditions under which curved
(non Ricci flat) supersymmetric domain wall solutions may exist. These curved
BPS domain wall solutions may, in general, be supported by non-constant vector
and hyper scalar fields. We establish our results by a careful analysis of the
BPS equations as well as of the associated integrability conditions and the
equations of motion. We construct an example of a curved BPS solution in a
gauged supergravity model with one hypermultiplet. We also discuss the dual
description of curved BPS domain walls in terms of RG flows.
