Induced Matter: Curved N-Manifolds Encapsulated In Riemann-Flat N+1 Dimensional Space

Authors

Harry I. Ringermacher, General Electric Global Research CenterFollow
Lawrence R. Mead, University of Southern MississippiFollow

Document Type

Article

Publication Date

10-1-2005

Department

Physics and Astronomy

School

Mathematics and Natural Sciences

Abstract

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.

Comments

©Journal of Mathematical Physics
DOI: 10.1063/1.2042968

Publication Title

Journal of Mathematical Physics

Volume

46

Issue

10

Recommended Citation

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