X iv : g r - qc / 0 51 10 12 v 1 2 N ov 2 00 5 Induced matter : Curved N - manifolds encapsulated in Riemann - flat N + 1 dimensional space

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann-flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1 dimensional Riemann-flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to “induce matter” in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space. PACS: 04.50.+h, 04.20.Jb, 04.20-q, 02.40.Ky Communications to [email protected]