Exploiting Symmetry in Applied and Numerical Analysis (E. Allgower et al eds.) 1992 AMS-SIAM Summer Seminar Proceedings. Lectures in Appl. Math. 29 (1993) 163-169
Michael Dellnitz and Ian Melbourne
Abstract
The classical Darboux Theorem states that symplectic forms are locally constant up to isomorphism, or equivalently that any two symplectic forms are locally isomorphic. We consider the corresponding results for symplectic forms that are invariant under the action of a compact Lie group. In this context, it is still true that symplectic forms are locally constant up to isomorphism but it is not true that any two symplectic forms are locally isomorphic.