On 4-dimensional cosmological models locally embedded in a 5-dimensional   Ricci-flat space
  We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction is performed in the Jordan frame according to the induced-matter theory of Wesson. 
A. G. Agnese and M. La Camera