ISSN : 1226-0657
A symplectic manifold is a pair (M, <TEX>$\omega$</TEX>) consisting of a smooth manifold M and a non-degenerate closed 2-form <TEX>$\omega$</TEX> on M. Locally, <TEX>$\omega$</TEX> = (equation omitted) and d<TEX>$\omega$</TEX> = 0, when n = dimM. The condition d<TEX>$\omega$</TEX> = 0 implies that locally <TEX>$\omega$</TEX> = d<TEX>${\alpha}$</TEX> with <TEX>${\alpha}$</TEX> = (equation omitted). There are three main sources of symplectic manifolds.(omitted)