  We generalise the standard, flat p-brane solutions sourced by a dilaton and a
form field, by taking the worldvolume to be a curved Einstein space, such as
(anti-)de Sitter space. Our method is based on reducing the p-branes to domain
walls and then allowing these domain walls to be curved. For de Sitter
worldvolumes this extends some recently constructed warped de Sitter
non-compactifications. We restrict our analysis to solutions that possess
scaling behavior and demonstrate that these scaling solutions are near-horizon
limits of a more general solution. Finally, our framework can equally be used
for spacelike branes and the uplift of the domain wall/cosmology correspondence
becomes in this context a more general timelike/spacelike brane correspondence.
