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Seminar on the Embedding Problem Introduction

Seminar on the Embedding Problem Introduction Introduction In the 1925 preface to his textbook on "Riemannian Geometry," L. P. Eisenhart was noting that, "The recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject." In such a context, he devoted a large part of the book to the description of Riemann spaces em- bedded in flat spaces with added dimensionality. It turned out, however, that general relativity was handy enough when treated in terms of the curvilinear coordi- nates of the Riemann space itself; the embedding seemed to add extraneous spatial extensions which added little to the understanding of gravitation and the cosmology. From time to time, some interesting results would be derived in this way, but they would also be directly derivable from the Riemannian metric, interest in the embedding thus subsiding again. An example of this sort was provided by C. Fronsdal's study of the complete Schwarzschild solution via its embedding [Phys. Rev. 116, 778 (1958)]; the remarkable insight into that problem did not give rise to an interest in the embedding method, since the same result was achieved * Held at the Southwest Center for Advanced Studies, Dallas, Texas. shortly afterward by M. D. Kruskal http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reviews of Modern Physics American Physical Society (APS)

Seminar on the Embedding Problem Introduction

ROBINSON, I; NE'EMAN, Y
Reviews of Modern Physics , Volume 37 (1) – Jan 1, 1965
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1965 The American Physical Society
ISSN
1539-0756
DOI
10.1103/RevModPhys.37.201
Publisher site
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Abstract

Introduction In the 1925 preface to his textbook on "Riemannian Geometry," L. P. Eisenhart was noting that, "The recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject." In such a context, he devoted a large part of the book to the description of Riemann spaces em- bedded in flat spaces with added dimensionality. It turned out, however, that general relativity was handy enough when treated in terms of the curvilinear coordi- nates of the Riemann space itself; the embedding seemed to add extraneous spatial extensions which added little to the understanding of gravitation and the cosmology. From time to time, some interesting results would be derived in this way, but they would also be directly derivable from the Riemannian metric, interest in the embedding thus subsiding again. An example of this sort was provided by C. Fronsdal's study of the complete Schwarzschild solution via its embedding [Phys. Rev. 116, 778 (1958)]; the remarkable insight into that problem did not give rise to an interest in the embedding method, since the same result was achieved * Held at the Southwest Center for Advanced Studies, Dallas, Texas. shortly afterward by M. D. Kruskal

Journal

Reviews of Modern Physics – American Physical Society (APS)

Published: Jan 1, 1965

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