Arms, Judith M. and Marsden, Jerrold E. and Moncrief, Vincent
(1981)
*Symmetry and Bifurcations of Momentum Mappings.*
Communications in Mathematical Physics, 78
(4).
pp. 455-478.
ISSN 0010-3616.
http://resolver.caltech.edu/CaltechAUTHORS:20100712-140837776

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## Abstract

The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.

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Additional Information: | © Springer-Verlag 1981. Received January 31, 1980. This work was partially supported by the National Science Foundation. The second author was supported by a Killam Visiting fellowship at the University of Calgary during the completion of the paper. It is a pleasure to thank M. Berger, M. Buchner, Y. Choquet-Bruhat, A. Fischer, M. Gotay, R.Jackiw, L.Nirenberg, S. Schecter, I. Singer, J. Sniatycki, F. Tipler, W. Tulczyjew, and A. Weinstein for their interest in this work and their comments. Communicated by A. Jaffe | |||||||||

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Deposited By: | Ruth Sustaita | |||||||||

Deposited On: | 13 Jul 2010 15:48 | |||||||||

Last Modified: | 26 Dec 2012 12:13 |

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