A class of five-dimensional space-times that contain four-dimensional
hypersurfaces whose intrinsic metrics are of cosmological interest is
investigated. First, the five-dimensional space-time is assumed to be
Riemann flat-the problem of determining the intrinsic metrics of the f
our-dimensional hypersurfaces then becomes a problem of embedding in f
lat space-time. Second, the Riemann flat solutions are used as a start
ing point to find solutions to Einstein's vacuum field equations in fi
ve dimensions that are not Riemann flat. In particular, a new general
class of five-dimensional vacuum solutions is found. (C) 1996 American
Institute of Physics.