  Phase space is the state space of classical mechanics, and this manifold is
normally endowed only with a symplectic form. The geometry of quantum mechanics
is necessarily more complicated. Arguments will be given to show that
augmenting the symplectic manifold of classical phase space with a Riemannian
metric is sufficient for describing quantum mechanics. In particular, using
such spaces, a fully satisfactory geometric version of quantization will be
developed and described.
