Generalizing the notion of curvature collineations a symmetry called “curvature inheritance” (CI) is introduced, defined by a vector field \(\xi\), satisfying \(L_ \xi R^ a_{bcd}=2\alpha R^ a_{bcd}\), where \(R^ a_{bcd}\) is the Riemann curvature tensor of a Riemannian space \(V_ n\), \(L_ \xi\) denotes the Lie derivative with respect to \(\xi\), and \(\alpha\neq 0\) is a scalar function. The connection between a CI and physically interesting conformal motions in a \(V_ 4\) is established, and it is shown that a CI, which is also a conformal Killing vector, can generate new and physically relevant solutions of Einstein’s field equations for a variety of fluid space times.