Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 1974 | public
Journal Article

Reduction of symplectic manifolds with symmetry

Abstract

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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023