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.
- Publication:
-
Reports on Mathematical Physics
- Pub Date:
- February 1974
- DOI:
- 10.1016/0034-4877(74)90021-4
- Bibcode:
- 1974RpMP....5..121M