Contact Weyl Manifold over a Symplectic Manifold

Abstract

We give a brief review on Weyl manifolds and thier Poincare-Cartan classes. A Weyl manifold is a Weyl algebra bundle over a symplectic manifold which is a geometrization of deformation quantization and the Poincare-Cartan class is a complete invariant of Weyl manifolds. We introduce a concept of a contact Weyl manifold, which is a contact algebra bundle over a symplectic manifold containing a Weyl manifold as a subbundle. We show the existence of contact Weyl manifolds for a symplectic manifold. We construct a connection on a contact Weyl manifold which gives a Fedosov connection when it is restricted to a Weyl manifold. With the help of the connection, we show that the cohomology class given by the curvature of Fedosov connection coincides with the Poincare-Cartan class.