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Reduction of symplectic manifolds with symmetry

Marsden, Jerrold E. and Weinstein, Alan J. (1974) Reduction of symplectic manifolds with symmetry. Reports on Mathematical Physics, 5 (1). pp. 121-130. ISSN 0034-4877. doi:10.1016/0034-4877(74)90021-4.

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We give a unified framework for the construction of symplectic manifolds from systems with symmetries. Several physical and mathematical examples are given; for instance, we obtain Kostant’s result on the symplectic structure of the orbits under the coadjoint representation of a Lie group. The framework also allows us to give a simple derivation of Smale's criterion for relative equilibria. We apply our scheme to various systems, including rotationally invariant systems, the rigid body, fluid flow, and general relativity.

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Additional Information:© 1974 Published by Elsevier Science Ltd. Received September 15, 1972. Available online 22 March 2002. Partially supported by NSF Grant GP-15735. Partially supported by NSF Grant GP-34785x and a Sloan Fellowship.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19864
Deposited By: Ruth Sustaita
Deposited On:10 Sep 2010 18:00
Last Modified:08 Nov 2021 23:55

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