Physics and Astronomy
Mathematics and Natural Sciences
Liko and Wesson have recently introduced a new five-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann-flat five-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 submanifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space. (c) 2005 American Institute of Physics.
Journal of Mathematical Physics
Ringermacher, H. I.,
Mead, L. R.
(2005). Induced Matter: Curved N-Manifolds Encapsulated In Riemann-Flat N+1 Dimensional Space. Journal of Mathematical Physics, 46(10).
Available at: https://aquila.usm.edu/fac_pubs/2639