Hypersurfaces of Five Dimensional Space-times

It is shown that a space-time hypersurface of a 5-dimensional Ricci-flat space-time has its energy momentum tensor algebrically related to its extrinsic curvature and to the Riemann curvature of the embedding space. It is also seen that the Einstein-Maxwell field does not arise naturally from this geometry, so that a Kaluza-Klein model based on it would require further assumptions.