A Caltech Library Service

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.

[img] PDF - Published Version
Restricted to Repository administrators only
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription
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.
Funding AgencyGrant Number
Sloan FellowshipUNSPECIFIED
Record Number:CaltechAUTHORS:20100910-101924768
Persistent URL:
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:27 Jan 2015 18:28

Repository Staff Only: item control page