  We investigate an exact solution that describes the embedding of the
four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein
spacetime. The effective metric of the 4D perfect fluid as a hypersurface with
induced matter is equivalent to the Robertson-Walker metric of cosmology. This
general solution shows interconnections among many 5D solutions, such as the
solution in the braneworld scenario and the topological black hole with
cosmological constant. If the 5D cosmological constant is positive, the metric
periodically depends on the extra dimension. Thus we can compactify the extra
dimension on $S^1$ and study the phenomenological issues. We also generalize
the metric ansatz to the higher-dimensional case, in which the 4D part of the
Einstein equations can be reduced to a linear equation.
