On the Space of Riemannian Metrics on Symplectic and Contact Manifolds

Abstract

Let AMω be the space of all almost Kahlerian smooth metrics on a symplectic manifold M 2n ,ω such that the fundamental form of each metric coincides with ω. It is well known that AMω is a retractor of the space M of all smooth metrics on M. We show that M is a smooth trivial bundle over AMω. A similar fact holds also in the case of a contact manifold.